The phenomenology of glass-forming liquids is often described in terms of their underlying, high-dimensional potential energy surface. In particular, the statistics of stationary points sampled as a function of temperature provides useful insight into the thermodynamics and dynamics of the system. To make contact with the real space physics, however, analysis of the spatial structure of the normal modes is required. In this work, we numerically study the potential energy surface of a glass-forming ternary mixture. Starting from liquid configurations equilibrated over a broad range of temperatures using a swap Monte Carlo method, we locate the nearby stationary points and investigate the spatial architecture and the energetics of the associated unstable modes. Through this spatially-resolved analysis, originally developed to study local minima, we corroborate recent evidence that the nature of the unstable modes changes from delocalized to localized around the mode-coupling temperature. We find that the displacement amplitudes of the delocalized modes have a slowly decaying far field, whereas the localized modes consist of a core with large displacements and a rapidly decaying far field. The fractal dimension of unstable modes around the mobility edge is equal to 1, consistent with the scaling of the participation ratio. Finally, we find that around and below the mode-coupling temperature the unstable modes are localized around structural defects, characterized by a disordered local structure markedly different from the liquid's locally favored structure. These defects are similar to those associated to quasi-localized vibrations in local minima and are good candidates to predict the emergence of localized excitations at low temperature.
A key property of glass forming alloys, the anomalously small volume difference with respect to the crystal, is shown to arise as a direct consequence of the soft repulsive potentials between metals. This feature of the inter-atomic potential is demonstrated to be responsible for a significant component of the glass forming ability of alloys due to the decrease in the enthalpy of fusion and the associated depression of the freezing point.
The behaviour of a model glass forming liquid is analyzed for a range of densities, with a focus on the temperature interval where the liquid begins to display non-Arrhenius temperature dependence of relaxation times. Analyzing the dynamics along with properties of local potential energy minima sampled by the liquid, a crossover or onset temperature $T_s$ is identified below which the liquid manifests {\it slow dynamics}, and a change in the character of typical local potential energy minima.
We review the phenomena of dynamical heterogeneity in glass-forming systems and its description within replica and mean-field theories of the glass transition.
Glass-forming liquids display strong fluctuations -- dynamical heterogeneities -- near their glass transition. By numerically simulating a binary Weeks-Chandler-Andersen liquid and varying both temperature and timescale, we investigate the probability distributions of two kinds of local fluctuations in the non-equilibrium (aging) regime and in the equilibrium regime; and find them to be very similar in the two regimes and across temperatures. We also observe that, when appropriately rescaled, the integrated dynamic susceptibility is very weakly dependent on temperature and very similar in both…
We numerically study the zero-temperature relaxation dynamics of several glass-forming models to their inherent structures, following quenches from equilibrium configurations sampled across a wide range of initial temperatures. In a mean-field Mari-Kurchan model, we find that relaxation changes from a power-law to an exponential decay below a well-defined temperature, consistent with recent findings in mean-field $p$-spin models. By contrast, for finite-dimensional systems, the relaxation is always algebraic, with a non-trivial universal exponent at high temperatures crossing over to a harmoni…
Enormous enhancement in the viscosity of a liquid near its glass transition is generally connected to the growing many-body static correlations near the transition, often coined as `amorphous ordering'. Estimating the length scales of such correlations in different glass-forming liquids is highly important to unravel the physics of glass formation. Experiments on molecular glass-forming liquids become pivotal in this scenario as the viscosity grows several folds ($\sim 10^{14}$), simulations or colloidal glass experiments fail to access the long-time scales required. Here we design an experime…
We examine the relation between the free volume per particle and the variance of the particle position, equivalent to a local Debye-Waller (DW) factor for a 2D glass-forming alloy using molecular dynamics simulations. We find that the latter quantity exhibits significant spatial heterogeneity despite involving trajectories two orders of magnitude shorter than those typically used to measure such heterogeneities. We find that the free volume exhibits no significant spatial correlation with the local DW factor. We conclude that the spatial variation in local free volume is not the cause of the s…
Mixtures of glass-forming fluids sometimes exhibit glass-glass phase separation at low temperatures. Here, we use a molecular dynamics simulation to study one of the simplest examples of the glass-glass phase separation. We consider a mixture composed of type A and B particles, in which the A-A and B-B interactions are the identical Lennard-Jones interactions and the A-B interaction is repulsive only. To avoid crystallization, we also introduce the polydispersity in the particle sizes for each component. We study the phase separation kinetics of this model at a 50:50 concentration at various t…
The configurational entropy is one of the most important thermodynamic quantities characterizing supercooled liquids approaching the glass transition. Despite decades of experimental, theoretical, and computational investigation, a widely accepted definition of the configurational entropy is missing, its quantitative characterization remains fraud with difficulties, misconceptions and paradoxes, and its physical relevance is vividly debated. Motivated by recent computational progress, we offer a pedagogical perspective on the configurational entropy in glass-forming liquids. We first explain w…
We propose and numerically implement a local probe of the static self-induced heterogeneity characterizing glass-forming liquids. The method relies on the equilibrium statistics of the overlap between pairs of configurations measured in mesoscopic cavities with unconstrained boundaries. By systematically changing the location of the probed cavity, we directly detect spatial variations of the overlap fluctuations. We provide a detailed analysis of the statistics of a local estimate of the configurational entropy and we infer an estimate of the surface tension between amorphous states, ingredien…
We introduce a new quantity to probe the glass transition. This quantity is a linear generalized compressibility which depends solely on the positions of the particles. We have performed a molecular dynamics simulation on a glass forming liquid consisting of a two component mixture of soft spheres in three dimensions. As the temperature is lowered, the generalized compressibility drops sharply at the glass transition. Our results are consistent with the kinetic view of the glass transition, but not with an underlying second order phase transition.
Statistical Gauge Theory of Structural Glasses: Equilibrium Scenarios and Glass-Forming Ability
IMET UB RAS（俄罗斯科学院乌拉尔分院金属物理研究所）；Ural Federal University（乌拉尔联邦大学）；HPPI（高温等离子体物理研究所）；N. L. Dukhov Research Institute of Automatics (VNIIA)（N.L.杜霍夫自动技术研究院）
The term "fragility" describes the rate at which viscosity grows when a supercooled liquid approaches its putative glass transition temperature. The field of glassy materials is actively searching for a structural origin that governs this dynamical slowing down in the supercooled liquid, which occurs without any discernible change in structure. Our work shows clear evidence that growing many-body static amorphous order is intimately correlated with the kinetic fragility of glass-forming liquids. It confirms that the system's dynamical response to temperature is concealed in its micro-structure…
This is our reply to the comment by Sausset and Tarjus (arXiv:0802.1631) on our paper titled "Correlation between Dynamic Heterogeneity and Medium-Range Order in Two-Dimensional Glass-Forming Liquids" [Phys. Rev. Lett. Vol. 99, No. 21, 215701 (2007)].
We present molecular dynamics results for a two component, two-dimensional Lennard-Jones supercooled liquid near the glass transition. We find that the supercooled liquid is spatially heterogeneous and that there are long-lived clusters whose size distribution satisfies a scaling relation up to a cutoff. The similarity of several properties of the supercooled liquid to those of a mean-field glass-forming fluid near the spinodal suggests that the glass transition in the supercooled liquid is associated with an underlying thermodynamic instability.
We introduce an approach to derive an effective scalar field theory for the glass transition; the fluctuating field is the overlap between equilibrium configurations. We apply it to the case of constrained liquids for which the introduction of a conjugate source to the overlap field was predicted to lead to an equilibrium critical point. We show that the long-distance physics in the vicinity of this critical point is in the same universality class as that of a paradigmatic disordered model: the random-field Ising model. The quenched disorder is provided here by a reference equilibrium liquid c…
We introduce a new disordered system, the Super-Potts model, which is a more frustrated version of the Potts glass. Its elementary degrees of freedom are variables that can take M values and are coupled via pair-wise interactions. Its exact solution on a completely connected lattice demonstrates that for large enough M it belongs to the class of mean-field systems solved by a one step replica symmetry breaking Ansatz. Numerical simulations by the parallel tempering technique show that in three dimensions it displays a phenomenological behaviour similar to the one of glass-forming liquids. The …
A low temperature Monte Carlo dynamics of a Keating like oscillator model is used to study the relationship between the nature of glasses from the viewpoint of rigidity, and the strong-fragile behaviour of glass-forming liquids. The model shows that a Phillips optimal glass formation with minimal enthalpic changes is obtained under a cooling/annealing cycle when the system is optimally constrained by the harmonic interactions, i.e. when it is isostatically rigid. For these peculiar systems, the computed fragility shows also a minimum, which demonstrates that isostatically rigid glasses are str…
The effective potential formalism is applied to glass forming liquids, choosing a coupling potential such that the "order parameter", conjugated to the coupling strength, is the mean square displacement of the particles from their position in the quenched reference configuration. The potential is linear in some interval of its argument, signaling the coexistence of two phases in the system, one with low and one with high mean square displacement. Within this formalism, one can also compute the free energy of metastable states and their complexity.
We show that a glass transition, signaled by a peak in the specific heat vs. temperature, can occur because a glassy system that shows no signs of aging progresses so slowly through the energy landscape that the time needed to obtain an accurate estimate of the thermodynamic averages exceeds the observation time. We find that below the glass transition temperature of a three dimensional binary mixture of soft spheres, the specific heat increases with measurement time spans orders of magnitude longer than previously recognized equilibration times.
We introduce simple models, inspired by previous models for froths and covalent glasses, with trivial equilibrium properties but dynamical behaviour characteristic of strong glass forming systems. These models are also a generalization of backgammon or urn models to a non--constant number of particles, where entropic barriers are replaced by energy barriers, allowing for the existence of activated processes. We formulate a mean--field version of the models, which keeps most of the features of the finite dimensional ones, and solve analytically the out--of--equilibrium dynamics in the low tempe…
This article discusses recent attempts to provide a deeper understanding of the thermoreversible "gel" state of colloidal matter and to unravel the analogies between gels at the colloidal level and gels at the molecular level, commonly known as network-forming strong liquids. The connection between gel-forming patchy colloids and strong liquids is provided by the limited valence of the inter-particle interactions, i.e. by the presence of a limit in the number of bonded nearest neighbors.
We study the four-point dynamic susceptibility $χ_4(t)$ obtained from Brownian dynamics computer simulations of the Kob-Andersen Lennard-Jones mixture. We compare the results of the simulations with qualitative predictions of the mode-coupling theory. In addition, we test an estimate of the four-point susceptibility recently proposed by Berthier \textit{et al.} [Science, \textbf{310}, 1797 (2005)].
We use large scale computer simulations of a glass-forming liquid in which a fraction c of the particles has been permanently pinned. We find that the relaxation dynamics shows an exponential dependence on c. This result can be rationalized by means of a simple theoretical Ansatz and we discuss its implication for thermodynamic theories for the glass-transition. For intermediate and low temperatures we find that the slowing down of the dynamics due to the pinning saturates and that the cooperativity decreases with increasing c, results which indicate that in glass-forming liquids there is a dy…
Using computer simulations of an atomistic glass-forming liquid, we investigate the fluctuations of the overlap between a fluid configuration and a quenched reference system. We find that large fluctuations of the overlap develop as temperature decreases, consistent with the existence of the random critical point that is predicted by effective field theories. We discuss the scaling of fluctuations near the presumed critical point, comparing the observed behaviour with that of the random-field Ising model. We argue that this critical point directly reveals the existence of an interfacial tensio…
We identify a link between the glass transition and percolation of mobile regions in configuration space. We find that many hallmarks of glassy dynamics, for example stretched-exponential response functions and a diverging structural relaxation time, are consequences of the critical properties of mean-field percolation. Specific predictions of the percolation model include the range of possible stretching exponents $1/3 \leq β\leq 1$ and the functional dependence of the structural relaxation time $τ_α$ and exponent $β$ on temperature, density, and wave number.
A Monte Carlo method is used in order to simulate the competition between the molecular relaxation and crystallization times in the formation of a glass. The results show that nucleation is avoided during supercooling and produce self-organization in the sense of the rigidity theory, where the number of geometrical constraints due to bonding and excluded volume are compared with the degress of freedom available to the system. Following this idea, glass transitions were obtained by producing self-organization, and in the case of geometrical frustration, self-organization is naturally observed.
Thermal conductivity of a model glass-forming system in the liquid and glass states is studied using extensive numerical simulations. We show that near the glass transition temperture, where the structural relaxation time becomes very long, the measured thermal conductivity decreases with increasing age. Secondly the thermal conductivity of the disordered solid obtained at low temperatures depends on the cooling rate with which it was prepared, with lower cooling rates leading to lower thermal conductivity. Our analysis links this decrease of the thermal conductivity with increased exploration…
All liquids are topologically disordered materials; however, the degree of disorder can vary as a result of internal fluctuations in structure and topology. These fluctuations depend on both the composition and temperature of the system. Most prior work has considered the mean values of liquid or glass properties, such as the average number of topological degrees of freedom per atom; however, the localized fluctuations in properties also play a key role in governing the macroscopic characteristics of any glass-forming system. This paper proposes a generalized approach for modeling topological …
We introduce a new theoretical model of simple fluid, whose interactions, defined in terms of the Voronoi cells of the configurations, are local and many-body. The resulting system is studied both theoretically and numerically. We show that the fluid, though sharing the global features of other models of fluids with soft interactions, has several unusual characteristics, which are investigated and discussed.
Temporal relaxation of density fluctuations in supercooled liquids near the glass transition occurs in multiple steps. The short-time $β$-relaxation is generally attributed to spatially local processes involving the rattling motion of a particle in the transient cage formed by its neighbors. Using molecular dynamics simulations for three model glass-forming liquids, we show that the $β$-relaxation is actually cooperative in nature. Using finite-size scaling analysis, we extract a growing length-scale associated with $β$-relaxation from the observed dependence of the $β$-relaxation time on the …
If a liquid is cooled rapidly to form a glass, its structural relaxation becomes retarded, producing a drastic increase in viscosity. In two dimensions, strong long-wavelength fluctuations persist, even at low temperature, making it difficult to evaluate the microscopic structural relaxation time. This Letter shows that, in a 2D glass-forming liquid, relative displacement between neighbor particles yields a relaxation time that grows in proportion to the viscosity. In addition to thermal elastic vibrations, hydrodynamic fluctuations are found to affect the long-wavelength dynamics, yielding a …
Translational dynamics of two-dimensional glass forming fluids is strongly influenced by soft, long-wavelength fluctuations first recognized by D. Mermin and H. Wagner. As a result of these fluctuations, characteristic features of glassy dynamics, such as plateaus in the mean squared displacement and the self-intermediate scattering function, are absent in two dimensions. In contrast, Mermin-Wagner fluctuations do not influence orientational relaxation and well developed plateaus are observed in orientational correlation functions. It has been suggested that by monitoring translational motion …
We propose that the dynamics of supercooled liquids and the formation of glasses can be understood from the existence of a zero temperature dynamical critical point. To support our proposal, we derive from simple physical assumptions a dynamic field theory for supercooled liquids, which we study using the renormalization group (RG). Its long time behaviour is dominated by a zero temperature critical point, which for dimensions d > 2 belongs to the directed percolation universality class. Molecular dynamics simulations confirm the existence of dynamic scaling behaviour consistent with the RG pr…
The inherent structure approach, wherein thermodynamic and structural changes in glass forming liquids are analyzed in terms of local potential energy minima that the liquid samples, has recently been applied extensively to the study of thermodynamic aspects of glass forming liquids. The evalation of the configurational entropy, which arises from the multiplicity of local energy minima, plays a central role in such analyses. Results are presented here concerning the calculation of configurational entropy based on computer simulations of a model liquid, and the application of the inherent struc…
We propose a simple theory for the dynamics of model glass-forming fluids, which should be solvable using a mean-field-like approach. The theory is based on transparent physical assumptions, which can be tested in computer simulations. The theory predicts an ergodicity-breaking transition that is identical to the so-called dynamic transition predicted within the replica approach. Thus, it can provide the missing dynamic component of the random first order transition framework. In the large-dimensional limit the theory reproduces the result of a recent exact calculation of Maimbourg et al. [PRL…
Existence and growth of amorphous order in supercooled liquids approaching glass transition is a subject of intense research. Even after decades of work, there is still no clear consensus on the molecular mechanisms that lead to a rapid slowing down of liquid dynamics approaching this putative transition. The existence of a correlation length associated with amorphous order has recently been postulated and also been estimated using multi-point correlation functions which cannot be calculated easily in experiments. Thus the study of growing amorphous order remains mostly restricted to systems l…
We discuss the relaxation dynamics of a simple lattice gas model for glass-forming systems and show that with increasing density of particles this dynamics slows down very quickly. By monitoring the trajectory of tagged particles we find that their motion is very heterogeneous in space and time, leading to regions in space in which there is a fast dynamics and others in which it is slow. We determine how the geometric properties of these quickly relaxing regions depend on density and time. Motivated by this heterogeneous hopping dynamics, we use a simple model, a variant of a continuous time r…
A theory which uses data of the static pair-correlation function is developed to calculate quantities associated with the viscous slowing down of supercooled liquids. We calculate value of the energy fluctuations that determine the number of stable bonds a particle forms with neighbors from data of the structural relaxation time. The number of bonds and the activation energy for relaxation are shown to increase sharply in a narrow temperature range close to the glass temperature. The configurational entropy calculated from values of the configurational fluctuations is found in good agreement w…
Via molecular dynamics simulations of a generic glass former in the supercooled and normal liquid states, it is shown that spatial correlations of strain fluctuations exhibit a crossover from the well-established power-law $\sim 1/r^3$-decay at long wavelengths to an exponential behavior, $\sim \exp(-r/l_{\text {c}})$ at intermediate distances. The characteristic length of the exponential decay grows both with temperature and time via, $l_{\text {c}}^2 \propto D(T)\, t$, with $D(T)$ being the temperature-dependent diffusion coefficient. This suggests that the crossover between the power-law an…
Motivated by recent experimental studies probing i) the existence of a mobile layer at the free surface of glasses, and ii) the capillary leveling of polymer nanofilms, we study the evolution of square-wave patterns at the free surface of a generic glass-forming binary Lennard-Jones mixture over a wide temperature range, by means of molecular dynamics simulations. The pattern's amplitude is monitored and the associated decay rate is extracted. The evolution of the latter as a function of temperature exhibits a crossover between two distinct behaviours, over a temperature range typically bounde…
We propose and use a novel, hybrid Monte Carlo algorithm that combines configurational bias particle swaps with parallel tempering. We use this new method to simulate a standard model of a glass forming binary mixture above and below the so-called mode-coupling temperature, Tmct. We find that an ansatz that was used previously to extrapolate thermodynamic quantities to temperatures below Tmct breaks down in the vicinity of the mode-coupling temperature. Thus, previous estimates of the so-called Kauzmann temperature need to be reexamined. Also, we find that the Adam-Gibbs relations D ~ exp(-a/T…
A multi-time probing of density fluctuations is introduced to investigate hidden time scales of heterogeneous dynamics in glass-forming liquids. Molecular dynamics simulations for simple glass-forming liquids are performed, and a three-time correlation function is numerically calculated for general time intervals. It is demonstrated that the three-time correlation function is sensitive to the heterogeneous dynamics and that it reveals couplings of correlated motions over a wide range of time scales. Furthermore, the time scale of the heterogeneous dynamics $τ_{\rm hetero}$ is determined by the…
We present evidence in favor of the possibility of treating an out-of-equilibrium supercooled simple liquid as a system in quasi-equilibrium. Two different temperatures, one controlled by the external bath and one internally selected by the system characterize the quasi-equilibrium state. The value of the internal temperature is explicitly calculated within the inherent structure thermodynamic formalism. We find that the internal temperature controls the relation between the response to an external perturbation and the long-time decay of fluctuations in the liquid.
We show by means of a Monte Carlo simulation study that three-dimensional models with long-range frustration display the generic phenomena seen in fragile glassforming liquids. Due to their properties (absence of quenched disorder, physical motivation in terms of structural frustration, and tunable fragility), these systems appear as promising minimal theoretical models for describing the glass transition of supercooled liquids.
We investigate the statistical mechanics of glass-forming materials and jamming matter by means of a geometrically driven approach based on a revised cell theory. By considering the system as constituted of jammed blocks of increasing sizes, we obtain a unified picture that describes accurately the whole process from low densities to limit densities at the glass/jamming transition. The approach retrieves many of the aspects of existing theories unifying them into a coherent framework. In particular, at low densities we find a free volume regime, based on local relaxation process, at intermedia…
It was recently shown that the real part of the frequency-dependent fluidity for several glass-forming liquids of different chemistry conforms to the prediction of the random barrier model (RBM) devised for ac electrical conduction in disordered solids [S. P. Bierwirth \textit{et al.}, Phys. Rev. Lett. {\bf 119}, 248001 (2017)]. Inspired by these results we introduce a crystallization-resistant modification of the Kob-Andersen binary Lennard-Jones mixture for which the results of extensive graphics-processing unit (GPU)-based molecular-dynamics simulations are presented. We find that the low-t…
We introduce a new quantity to probe the glass transition. This quantity is a linear generalized compressibility which depends solely on the positions of the particles. We have performed a molecular dynamics simulation on a glass forming liquid consisting of a two component mixture of soft spheres in three dimensions. As the temperature is lowered (or as the density is increased), the generalized compressibility drops sharply at the glass transition, with the drop becoming more and more abrupt as the measurement time increases. At our longest measurement times, the drop occurs approximately at…
We investigate the characteristic length scales associated with the glass transition phenomenon. By studying an atomic glass-forming liquid in negatively curved space, for which the local order is well identified and the amount of frustration opposing the spatial extension of this order is tunable, we provide insight into the structural origin of the main characteristics of the dynamics leading to glass formation. We find that the structural length and the correlation length characterizing the increasing heterogeneity of the dynamics grow together as temperature decreases. However, the system …
We analyse numerically thermal fluctuations of the static overlap between equilibrium configurations in a glass-forming liquid approaching the glass transition. We find that the emergence of slow dynamics near the onset temperature correlates with the development of non-Gaussian probability distributions of overlap fluctuations, measured using both annealed and quenched definitions. Below a critical temperature, a thermodynamic field conjugate to the overlap induces a first-order phase transition, whose existence we numerically demonstrate in the annealed case. These results establish that the…
The Shintani-Tanaka model is a glass-forming system whose constituents interact via anisotropic potential depending on the angle of a unit vector carried by each particle. The decay of time-correlation functions of the unit vectors exhibits the characteristics of generic relaxation functions during glass transitions. In particular it exhibits a 'stretched exponential' form, with the stretching index beta depending strongly on the temperature. We construct a quantitative theory of this correlation function by analyzing all the physical processes that contribute to it, separating a rotational fr…
We show how dynamical heterogeneities in glass forming systems emerge as a consequence of the existence of dynamical constraints, and we offer an interpretation of the glass transition as an entropy crisis in trajectory space (space-time) rather than in configuration space. To illustrate our general ideas, we analyze the one dimensional (d=1) Fredrickson-Andersen and East models. Dynamics of such dynamically constrained systems are shown to be isomorphic to the statics of d+1 dimensional dense mixtures of polydisperse non-interpenetrating domains. The domains coincide with arrested regions in …
In the context of a classical example of glass-formation in 3-dimensions we exemplify how to construct a statistical mechanical theory of the glass transition. At the heart of the approach is a simple criterion for verifying a proper choice of up-scaled quasi-species that allow the construction of a theory with a finite number of 'states'. Once constructed, the theory identifies a typical scale $ξ$ that increases rapidly with lowering the temperature and which determines the $α$-relaxation time $τ_α$ as $τ_α\sim \exp(μξ/T)$ with $μ$ a typical chemical potential. The theory can predict relaxati…
The excess heat capacity at glass transition temperature in two types of glass-forming systems of [xNaNO3\cdot(1-x)KNO3]60[Ca(NO3)2]40 (0 \leq x \leq 1) and Ca(NO3)2\cdotyH2O (4 \leq y \leq 13) is studied. In the former system, with the replacement of K+ cation with Na+ cation, the excess heat capacity is almost invariable around 65.1 J\cdotmol-1\cdotK-1, while the excess increases by 38.9 J\cdotmol-1\cdotK-1 with the increasing per molar H2O content in latter system. A quantitative description of the excess heat capacity is built up with the consideration of atomic and molecular translational…
We study by molecular dynamics computer simulation a binary soft-sphere mixture that shows a pronounced decoupling of the species' long-time dynamics. Anomalous, power-law-like diffusion of small particles arises, that can be understood as a precursor of a double-transition scenario, combining a glass transition and a separate small-particle localization transition. Switching off small-particle excluded-volume constraints slows down, rather than enhances, small-particle transport. The data are contrasted with results from the mode-coupling theory of the glass transition.
In this paper a simple model is proposed to decribe the spontaneous formation of coalitions among a group of actors like countries. The basic ingredients are from the physics of disorder systems. It is the interplay of two different spin glass models with respectively random bond and random site disorders which is instrumental in the present approach. The cold war stabilty period is then given an explanation as well the instabilities produced by the Warsow pact dissolution. European and Chinese stabilities are also discussed.
