Long-range spin glass in a field at zero temperature
International Research Center of Complexity Sciences, Hangzhou International Innovation Institute, Beihang University（北京航空航天大学杭州创新研究院复杂性科学国际研究中心）；ISC-CNR, UOS Rome, Sapienza Università di Roma（罗马智慧大学罗马单元意大利国家研究委员会凝聚态物理系统研究所）；Dipartimento di Fisica, Sapienza Università di Roma（罗马智慧大学物理系）；INFN-Sezione di Roma 1（罗马第一意大利国家核物理研究所）；Nanotec-CNR, UOS Rome, Sapienza Università di Roma（罗马智慧大学罗马单元意大利国家研究委员会纳米技术研究所）
Maria Chiara Angelini, Saverio Palazzi, Giorgio Parisi, Tommaso Rizzo
We compute the critical exponents of the zero-temperature spin glass transition in a field on a one-dimensional long-range model, a proxy for higher-dimensional systems. Our approach is based on a novel loop expansion within the Bethe $M$-layer formalism, whose adaptation to this specific case is detailed here. The resulting estimates provide crucial benchmarks for numerical simulations that can access larger system sizes in one dimension, thus offering a key test of the theory of spin glasses in a field.
We numerically study finite-dimensional spin glasses at low and zero temperature, finding evidences for (i) strong time/space heterogeneities, (ii) spontaneous time scale separation and (iii) power law distributions of flipping times. Using zero temperature dynamics we study blocking, clustering and persistence phenomena.
An approximate method is proposed for investigating complex-temperature properties of real-dimensional spin-glass models. The method uses the complex-temperature data of the ferromagnetic model on the same lattice. The universality line in the complex-temperature space is obtained.
We study spin-glass systems characterized by continuous occurrence of singularities. The theory of Lee-Yang zeros is used to find the singularities. By using the replica method in mean-field systems, we show that two-dimensional distributions of zeros of the partition function in a complex parameter plane are characteristic feature of random systems. The results of several models indicate that the concept of chaos in the spin-glass state is different from that of the replica symmetry breaking. We discuss that a chaotic phase at imaginary temperature is different from the spin-glass phase and i…
By using real space renormalisation group (RG) methods we show that spin-glasses in a field display a new kind of transition in high dimensions. The corresponding critical properties and the spin-glass phase are governed by two non-perturbative zero temperature fixed points of the RG flow. We compute the critical exponents, discuss the RG flow and its relevance for three dimensional systems. The new spin-glass phase we discovered has unusual properties, which are intermediate between the ones conjectured by droplet and full replica symmetry breaking theories. These results provide a new perspe…
The properties of discrete two-dimensional spin glasses depend strongly on the way the zero-temperature limit is taken. We discuss this phenomenon in the context of the Migdal-Kadanoff renormalization group. We see, in particular, how these properties are connected with the presence of a cascade of fixed points in the renormalization group flow. Of particular interest are two unstable fixed points that correspond to two different spin-glass phases at zero temperature. We discuss how these phenomena are related with the presence of entropy fluctuations and temperature chaos, and universality in…
We study the partition-function zeros in mean-field spin-glass models. We show that the replica method is useful to find the locations of zeros in a complex parameter plane. For the random energy model, we obtain the phase diagram in the plane and find that there are two types of distribution of zeros: two-dimensional distribution within a phase and one-dimensional one on a phase boundary. Phases with a two-dimensional distribution are characterized by a novel order parameter defined in the present replica analysis. We also discuss possible patterns of distributions by studying several systems…
We consider the zero-temperature dynamics for the infinite-range, non translation invariant one-dimensional spin model introduced by Marinari, Parisi and Ritort to generate glassy behaviour out of a deterministic interaction. It is shown that there can be a large number of metatastable (i.e., one-flip stable) states with very small overlap with the ground state but very close in energy to it, and that their total number increases exponentially with the size of the system.
We introduce the strongly-interacting trap model, a version of Bouchaud's trap model for glasses [Bouchaud J-P 1992 {\em J. Phys. I France {\bf 2}} 1705]. At finite temperatures the model exhibits glassy relaxation over intermediate timeframes but reaches a steady state at finite times. In limit of zero temperature and with a suitably renormalised timescale the model maps onto the Bak-Sneppen model, widely studied in the context of self-organised criticality [Bak P and Sneppen K 1993 {\em Phys. Rev. Lett. {\bf 71}} 4083]. Hence zero temperature is a critical point in all dimensions. These clai…
The zero temperature phase diagram of spin glasses on finite connectivity graphs is investigated, with or without magnetic field and/or ferromagnetic bias, for mean field (using the cavity method) and Edwards-Anderson (using numerical ground states computations) models. In the mean field case we show that the phase diagram is complex and compute the equivalent of the zero temperature de Almeida-Thouless line. In the 3d model however, we found a trivial phase diagram. This paper present new analytical results as well as a rapid review of numerical works on ground states.
By quenched-randomly mixing local units of different spatial dimensionalities, we have studied Ising spin-glass systems on hierarchical lattices continuously in dimensionalities 1 =< d =< 3. The global phase diagram in temperature, antiferromagnetic bond concentration, and spatial dimensionality is calculated. We find that, as dimension is lowered, the spin-glass phase disappears to zero temperature at the lower-critical dimension d_c=2.431. Our system being a physically realizable system, this sets an upper limit to the lower-critical dimension in general for the Ising spin-glass phase. As di…
We investigate partition-function zeros of the many-body interacting spherical spin glass, the so-called $p$-spin spherical model, with respect to the complex temperature in the thermodynamic limit. We use the replica method and extend the procedure of the replica symmetry breaking ansatz to be applicable in the complex-parameter case. We derive the phase diagrams in the complex-temperature plane and calculate the density of zeros in each phase. Near the imaginary axis away from the origin, there is a replica symmetric phase having a large density. On the other hand, we observe no density in t…
Zeros of the $n$th moment of the partition function $[Z^n]$ are investigated in a vanishing temperature limit $β\to \infty$, $n \to 0$ keeping $y=βn \sim O(1)$. In this limit, the moment parameterized by $y$ characterizes the distribution of the ground-state energy. We numerically investigate the zeros for $\pm J$ Ising spin glass models with several ladder and tree systems, which can be carried out with a feasible computational cost by a symbolic operation based on the Bethe--Peierls method. For several tree systems we find that the zeros tend to approach the real axis of $y$ in the thermodyn…
Zeros of the moment of the partition function $[Z^n]_{\bm{J}}$ with respect to complex $n$ are investigated in the zero temperature limit $β\to \infty$, $n\to 0$ keeping $y=βn \approx O(1)$. We numerically investigate the zeros of the $\pm J$ Ising spin glass models on several Cayley trees and hierarchical lattices and compare those results. In both lattices, the calculations are carried out with feasible computational costs by using recursion relations originated from the structures of those lattices. The results for Cayley trees show that a sequence of the zeros approaches the real axis of $…
We investigate the distribution of zeros of the partition function of the two- and three-dimensional symmetric $\pm J$ Ising spin glasses on the complex field plane. We use the method to analytically implement the idea of numerical transfer matrix which provides us with the exact expression of the partition function as a polynomial of fugacity. The results show that zeros are distributed in a wide region in the complex field plane. Nevertheless we observe that zeros on the imaginary axis play dominant roles in the critical behaviour since zeros on the imaginary axis are in closer proximity to …
We probe the droplet excitations in short range spin glasses by adding a perturbative long range interaction that decays with distance as a power law: $J/r^σ$. It is shown that if the power law exponent $σ$ is smaller than the spatial dimension $d$, the perturbation induces large scale avalanches which roll until they force the system to develop a pseudo gap in the excitation spectrum of the stabilities. This makes the perturbative long range interactions relevant for $σ< σ_c = d$. The droplet theory predicts that the critical exponent $σ_c$ depends on the droplet stiffness exponent as $σ_c=d-…
By making use of the Langevin dynamics and its generating functional (GF) formulation the influence of the long-range nature of the interaction on the tendency of the glass formation is systematically investigated. In doing so two types of models is considered: (i) the non-disordered model with a pure repulsive type of interaction and (ii) the model with a randomly distributed strength of interaction (a quenched disordered model). The long-ranged potential of interaction is scaled with a number of particles $N$ in such a way as to enable for GF the saddle-point treatment as well as the systema…
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.
Recent developments in study of two-dimensional spin glass models are reviewed in light of fractal nature of droplets at zero-temperature. Also presented are some new results including a new estimate of the stiffness exponent using a boundary condition different from conventional ones.
We conjecture the existence of a relationship between frustration and the transition point at zero temperature of Ising spin glasses. The relation reveals that, in several Ising spin glass models, the concentration of ferromagnetic bonds is close to the critical concentration at zero temperature when the output of a function about frustration is equal to unity. The function is the derivative of the average number of frustrated plaquettes with respect to the average number of antiferromagnetic bonds. This relation is conjectured in Ising spin glasses with binary couplings on two-dimensional lat…
The distribution of partition function zeros is studied for the $\pm J$ model of spin glasses on the Bethe lattice. We find a relation between the distribution of complex cavity fields and the density of zeros, which enables us to obtain the density of zeros for the infinite system size by using the cavity method. The phase boundaries thus derived from the location of the zeros are consistent with the results of direct analytical calculations. This is the first example in which the spin glass transition is related to the distribution of zeros directly in the thermodynamical limit. We clarify h…
The one-dimensional long-range Ising spin glass provides useful insights into the properties of finite dimensional spin glasses with short-range interactions. The defect energy renormalization group equations derived for it by Kotliar, Anderson and Stein have been re-examined and a new fixed point has been found. The fixed points which have previously been studied are found to be inappropriate. It is shown that the renormalization group equations themselves directly imply that the spin glass phase is replica symmetric, in agreement with droplet model expectations, when the range exponent $σ$ l…
In a finite-connectivity spin-glass at the zero-temperature limit, long-range correlations exist among the unfrozen vertices (whose spin values being non-fixed). Such long-range frustrations are partially removed through the first-step replica-symmetry-broken (1RSB) cavity theory, but residual long-range frustrations may still persist in this mean-field solution. By way of population dynamics, here we perform a perturbation-percolation analysis to calculate the magnitude of long-range frustrations in the 1RSB solution of a given spin-glass system. We study two well-studied model systems, the m…
We investigate the validity of a zeroth thermodynamic law for non-equilibrium systems. In order to describe the thermodynamics of the glassy systems, it has been introduced an extra parameter, the effective temperature which generalizes the fluctuation-dissipation theorem (FDT) to off-equilibrium systems and supposedly describes thermal fluctuations around the aging state. In particular we analyze two coupled systems of harmonic oscillators with Monte Carlo dynamics. We study in detail two types of dynamics: sequential dynamics, where the coupling between the subsystems comes only from the Ham…
The asymptotical behavior of physical quantities, like the order parameter, the replicon and longitudinal masses, is studied around the zero-field spin glass transition point when a small external magnetic field is applied. An effective field theory to model this asymptotics contains a small perturbation in its Lagrangian which breaks the zero-field symmetry. A first order renormalization group supplemented by perturbational results provides the scaling functions. The perturbative zero of the scaling function for the replicon mass defines a generic Almeida-Thouless surface stemming from the ze…
We consider the spin glass model in which the number of spin components, m, is infinite. In the formulation of the problem appropriate for numerical calculations proposed by several authors, we show that the order parameter defined by the long-distance limit of the correlation functions is actually zero and there is only "quasi long range order" below the transition temperature. We also show that the spin glass transition temperature is zero in three dimensions.
We discuss mean field theory of glasses without quenched disorder focusing on the justification of the replica approach to thermodynamics. We emphasize the assumptions implicit in this method and discuss how they can be verified. The formalism is applied to the long range Ising model with orthogonal coupling matrix. We find the one step replica-symmetry breaking solution and show that it is stable in the intermediate temperature range that includes the glass state but excludes very low temperatures. At very low temperatures this solution becomes unstable and this approach fails.
We uncover a new kind of entropic long range order in finite dimensional spin glasses. We study the link-diluted version of the Edwards-Anderson spin glass model with bimodal couplings (J=+/-1) on a 3D lattice. By using exact reduction algorithms, we prove that there exists a region of the phase diagram (at zero temperature and link density low enough), where spins are long range correlated, even if the ground states energy stiffness is null. In other words, in this region twisting the boundary conditions cost no energy, but spins are long range correlated by means of pure entropic effects.
We use Monte Carlo simulations to study the one-dimensional long-range diluted Heisenberg spin glass with interactions that fall as a power, sigma, of the distance. Varying the power is argued to be equivalent to varying the space dimension of a short-range model. We are therefore able to study both the mean-field and non-mean-field regimes. For one value of sigma, in the non-mean-field regime, we find evidence that the chiral glass transition temperature may be somewhat higher than the spin glass transition temperature. For the other values of sigma we see no evidence for this.
We study the transition of short range Ising spin glasses in a magnetic field, within a general replica symmetric field theory, which contains three masses and eight cubic couplings, that is defined in terms of the fields representing the replicon, anomalous and longitudinal modes. We discuss the symmetry of the theory in the limit of replica number n to 0, and consider the regular case where the longitudinal and anomalous masses remain degenerate. The spin glass transitions in zero and non-zero field are analyzed in a common framework. The mean field treatment shows the usual results, that is…
Scaling arguments and precise simulations are used to study the square lattice $\pm J$ Ising spin glass, a prototypical model for glassy systems. Droplet theory predicts, and our numerical results show, entropically-stabilized long range spin glass order at zero temperature. The low temperature scaling behavior has an important new crossover length scale that produces a power-law dependence of the heat capacity on temperature.
Monte Carlo studies of the 3D random field $XY$ model on simple cubic lattices of size $64^3$, using two different isotropic random-field probability distributions of moderate strength, show a glassy freezing behavior above $T_c$, and long-range order below $T_c$, consistent with our earlier results for weaker and stronger random fields. This model should describe random pinning in vortex lattices in type-II superconducting alloys, charge-density wave materials, and decagonal quasicrystals.
We compare the critical behavior of the short-range Ising spin glass with a spin glass with long-range interactions which fall off as a power sigma of the distance. We show that there is a value of sigma of the long-range model for which the critical behavior is very similar to that of the short-range model in four dimensions. We also study a value of sigma for which we find the critical behavior to be compatible with that of the three dimensional model, though we have much less precision than in the four-dimensional case.
I present a new method to analyze Glauber dynamics of the Sherrington-Kirkpatrick (SK) spin glass model. The method is based on ideas used in the classical kinetic theory of fluids. I apply it to study spin correlations in the high temperature phase ($T\ge T_c$) of the SK model at zero external field. The zeroth order theory is equivalent to a disorder dependent local equilibrium approximation. Its predictions agree well with computer simulation results. The first order theory involves coupled evolution equations for the spin correlations and the dynamic (excess) parts of the local field distr…
The zero-point entropy of a spin glass is a difficult property to experimentally determine and interpret. Spin glass theory provides various predictions, including unphysical ones, for the value of the zero-point entropy, however experimental results have been lacking. We have investigated the magnetic properties and zero-point entropy of two spinel Cu2+ based spin glasses, CuGa2O4 and CuAl2O4. Dc- and ac-susceptibility and specific heat measurements show many characteristic spin glass features for both materials. The spin glass freezing temperature is determined to be Tf = 2.89 +/- 0.05 K for…
We compare ground state properties of 3D Ising Spin Glasses with Gaussian couplings with results from off-equilibrium numerical simulations at non zero (but low) temperatures. We find that the non-zero temperature properties of the system smoothly connect to the T=0 behavior, confirming the point of view that results established at T=0 typically also give relevant information about the $T\ne 0$ physics of the system.
The spin-glass transition in a field in finite dimension is analyzed directly at zero temperature using a perturbative loop expansion around the Bethe lattice solution. The loop expansion is generated by the $M$-layer construction whose first diagrams are evaluated numerically and analytically. The generalized Ginzburg criterion reveals that the upper critical dimension below which mean-field theory fails is $D_U \le 8$, at variance with the classical result $D_U = 6$ yielded by finite-temperature replica field theory. Our expansion around the Bethe lattice has two crucial differences with res…
We present experimental results attempting to fingerprint nonanalyticities in the magnetization curves of spin glasses found by Katzgraber et al. [Phys. Rev. Lett. 89, 257202 (2002)] via zero-temperature Monte Carlo simulations of the Edwards-Anderson Ising spin glass. Our results show that the singularities at zero temperature due to the reversal-field memory effect are washed out by the finite temperatures of the experiments. The data are analyzed via the first order reversal curve (FORC) magnetic fingerprinting method. The experimental results are supported by Monte Carlo simulations of the…
We probe the energy landscape of the 3D Edwards-Anderson spin glass in a magnetic field to test for a spin glass ordering. We find that the spin glass susceptibility is anomalously large on the lattice sizes we can reach. Our data suggest that a transition from the spin glass to the paramagnetic phase takes place at B_c=0.65, though the possibility B_c=0 cannot be excluded. We also discuss the question of the nature of the putative frozen phase.
We investigate the ground state structure of the three-dimensional Ising spin glass in zero field by determining how the ground state changes in a fixed finite block far from the boundaries when the boundary conditions are changed. We find that the probability of a change in the block ground state configuration tends to zero as the system size tends to infinity. This indicates a trivial ground state structure, as predicted by the droplet theory. Similar results are also obtained in two dimensions.
Bethe Lattice Spin Glasses (BLSG) are models with finite connectivity which undergo a Replica Symmetry Breaking (RSB) phase transition in field, even at zero temperature. The order parameter describing this phase is a function related to the non-trivial organization of the states. We compute numerically the spin glass order parameter at zero temperature in BLSG with coordination number $z=3$ and couplings $J=\pm1$, near the transition. The method is based on a universal formula which relates the order parameter to the joint probability distribution of the energy gaps of the lowest lying states…
A unique analytical result for the Migdal-Kadanoff hierarchical lattice is obtained. The scaling of the defect energy for a zero-dimensional spin glass is derived for a bond distribution that is continuous at the origin. The value of the ``stiffness'' exponent in zero dimensions, y_0=-1, corresponds to the value also found in one dimension. This result complements and completes earlier findings for y_d at d>0.
We investigate the zero-temperature glassy transitions in the square-lattice +- J Ising model, with bond distribution $P(J_{xy}) = p δ(J_{xy} - J) + (1-p) δ(J_{xy} + J)$; p=1 and p=1/2 correspond to the pure Ising model and to the Ising spin glass with symmetric bimodal distribution, respectively. We present finite-temperature Monte Carlo simulations at p=4/5, which is close to the low-temperature paramagnetic-ferromagnetic transition line located at p=0.89, and at p=1/2. Their comparison provides a strong evidence that the glassy critical behavior that occurs for $1-p_0<p<p_0$, $p_0=0.897$, i…
We investigate dynamic scaling properties of the two-dimensional gauge glass model for the vortex glass phase in superconductors with quenched disorder. From extensive Monte Carlo simulations we obtain static and dynamic finite size scaling behavior, where the static simulations use a temperature exchange method to ensure convergence at low temperatures. Both static and dynamic scaling of Monte Carlo data is consistent with a glass transition at zero temperature. We study a dynamic correlation function for the superconducting order parameter, as well as the phase slip resistance. From the scal…
We show that the effective action of the quantum spherical spin glass is invariant under a generalized form of the Becchi-Rouet-Stora-Tyutin(BRST) supersymmetry. The Ward identities associated to this invariance indicate that the spin glass order parameter must vanish, and as a result the annealed average is exact in this model. We present new results for for the free energy, entropy and specific heat. Due to quantum effects the entropy remains finite and the specific het vanishes at zero temperature. results for the phase diagram coincide with those obtained by different formalisms. At zero t…
For many real spin-glass materials, the Edwards-Anderson model with continuous-symmetry spins is more realistic than the rather better understood Ising variant. In principle, the nature of an occurring spin-glass phase in such systems might be inferred from an analysis of the zero-temperature properties. Unfortunately, with few exceptions, the problem of finding ground-state configurations is a non-polynomial problem computationally, such that efficient approximation algorithms are called for. Here, we employ the recently developed genetic embedded matching (GEM) heuristic to investigate the n…
The stability of the spin-glass phase against a magnetic field is studied in the three and four dimensional Edwards-Anderson Ising spin glasses. Effective couplings and effective fields associated with length scale L are measured by a numerical domain-wall renormalization group method. The results obtained by scaling analysis of the data strongly indicate the existence of a crossover length beyond which the spin-glass order is destroyed by field H. The crossover length well obeys a power law of H which diverges as H goes to zero but remains finite for any non-zero H, implying that the spin-gla…
We analize the statistical mechanics of a long-range antiferromagnetic model defined on a D-dimensional hypercube, both at zero and finite temperatures. The associated Hamiltonian is derived from a recently proposed complexity measure of Boolean functions, in the context of neural networks learning processes. We show that, depending of the value of D, the system either presents a low temperature antiferromagnetic stable phase or the global antiferromagnetic order disappears at any temperature. In the last case the ground state is an infinitely degenerated non-glassy one, composed by two equal …
We review our earlier studies on the order parameter distribution of the quantum Sherrington-Kirkpatrick (SK) model. Through Monte Carlo technique, we investigate the behavior of the order parameter distribution at finite temperatures. The zero temperature study of the spin glass order parameter distribution is made by the exact diagonalization method. We find in low-temperature (high-transverse-field) spin glass region, the tail (extended up to zero value of order parameter) and width of the order parameter distribution become zero in thermodynamic limit. Such observations clearly suggest the…
We investigate the ground state structure of Ising spin glasses in zero magnetic field by determining how the ground state changes in a fixed finite block far from the boundaries when the boundary conditions are changed. We find, both in two and three dimensions, that the probability of a change in the block ground state configuration tends to zero as the system size tends to infinity. This indicates a trivial ground state structure, as predicted by the droplet theory.
For Gaussian Spin Glasses in low dimensions, we introduce a simple Strong Disorder renormalization procedure at zero temperature. In each disordered sample, the difference between the ground states associated to Periodic and Anti-Periodic boundary conditions defines a system-size Domain Wall. The numerical study in dimensions $d=2$ (up to sizes $2048^2$) and $d=3$ (up to sizes $128^3$) yields fractal Domain Walls of dimensions $d_s(d=2) \simeq 1.27$ and $d_s(d=3) \simeq 2.55$ respectively.
The zero-temperature critical state of the two-dimensional gauge glass model is investigated. It is found that low-energy vortex configurations afford a simple description in terms of gapless, weakly interacting vortex-antivortex pair excitations. A linear dielectric screening calculation is presented in a renormalization group setting that yields a power-law decay of spin-wave stiffness with distance. These properties are in agreement with low-temperature specific heat and spin-glass susceptibility data obtained in large-scale multi-canonical Monte Carlo simulations.
The paper contains a rigorous proof of the absence of quasi-long-range order in the random-field O(N) model for strong disorder in the space of an arbitrary dimensionality. This result implies that quasi-long-range order inherent to the Bragg glass phase of the vortex system in disordered superconductors is absent as the disorder or external magnetic field is strong.
Different sets of metastable states can be reached in glassy systems below some transition temperature depending on initial conditions and details of the dynamics. This is investigated for the Sherrington-Kirkpatrick spin glass model with long ranged interactions. In particular, the time dependent local field distribution and energy are calculated for zero temperature. This is done for a system quenched to zero temperature, slow cooling or simulated annealing, a greedy algorithm and repeated tapping. Results are obtained from Monte-Carlo simulations and a Master-Fokker-Planck approach. A compa…
At zero temperature, two-dimensional Ising spin glasses are known to fall into several universality classes. Here we consider the scaling at low but non-zero temperature and provide numerical evidence that $η\approx 0$ and $ν\approx 3.5$ in all cases, suggesting a unique universality class. This algebraic (as opposed to exponential) scaling holds in particular for the $\pm J$ model, with or without dilutions and for the plaquette diluted model. Such a picture, associated with an exceptional behavior at T=0, is consistent with a real space renormalization group approach. We also explain how the…
We study how the ground state of the two-dimensional Ising spin glass with Gaussian interactions in zero magnetic field changes on altering the boundary conditions. The probability that relative spin orientations change in a region far from the boundary goes to zero with the (linear) size of the system L like L^{-lambda}, where lambda = -0.70 +/- 0.08. We argue that lambda is equal to d-d_f where d (=2) is the dimension of the system and d_f is the fractal dimension of a domain wall induced by changes in the boundary conditions. Our value for d_f is consistent with earlier estimates. These res…
By connecting realistic spin glass models at low temperature to the highly disordered model at zero temperature, we argue that ordinary Edwards-Anderson spin glasses below eight dimensions have at most a single pair of physically relevant pure states at nonzero low temperature. Less likely scenarios that evade this conclusion are also discussed.
Three different vortex glass models are studied by examining the energy barrier against vortex motion across the system. In the two-dimensional gauge glass this energy barrier is found to increase logarithmically with system size which is interpreted as evidence for a low-temperature phase with zero resistivity. Associated with the large energy barriers is a breaking of ergodicity which explains why the well established results from equilibrium studies could fail. The behavior of the more realistic random pinning model is however different with decreasing energy barriers a no finite critical t…
