In structurally disordered ferromagnets the weak random dipole-dipole exchange may transform the polydomain state into a spin-glass one. To some extent the properties of such phase in disordered isotropic ferromagnet can be qualitatively described by the spherical model with the short-range ferromagnetic interaction and weak frustrated infinite-range random-bond exchange. This model is shown to predict that spin-glass phase substitute the ferromagnetic one at the arbitrary small disorder strength and that its thermodynamics has some similarity to that of polydomain state along with some significant distinctions. In particular, the longitudinal susceptibility at small fields becomes frozen below transition point at a constant value depending on the disorder strength, while the third order nonlinear magnetic susceptibilitiy exhibits the temperature oscillations in small field near the transition point. The relation of these predictions to the experimental data for some disordered isotropic ferromagnets is discussed.
Using ground state computations, we study the transition from a spin glass to a ferromagnet in 3-d spin glasses when changing the mean value of the spin-spin interaction. We find good evidence for replica symmetry breaking up till the critical value where ferromagnetic ordering sets in, and no ferromagnetic spin glass phase. This phase diagram is in conflict with the droplet/scaling and mean field theories of spin glasses. We also find that the exponents of the second order ferromagnetic transition do not depend on the microscopic Hamiltonian, suggesting universality of this transition.
In this paper we study the phase diagram of the disordered Ising ferromagnet. Within the framework of the Gaussian variational approximation it is shown that in systems with a finite value of the disorder in dimensions D=4 and D < 4 the paramagnetic and ferromagnetic phases are separated by a spin-glass phase. The transition from paramagnetic to spin-glass state is continuous (second-order), while the transition between spin-glass and ferromagnetic states is discontinuous (first-order). It is also shown that within the considered approximation there is no replica symmetry breaking in the spin-…
We compare aging in a disordered ferromagnet and in a spin glass, by studying the different phases of a reentrant system. We have measured the relaxation of the low-frequency ac susceptibility, in both the ferromagnetic and spin-glass phases of a CdCr_{1.9}In_{0.1}S_4 sample. A restart of aging processes when the temperature is lowered (`chaos-like' effect) is observed in both phases. The memory of previous aging at a higher temperature can be retrieved upon re-heating, but in the ferromagnetic phase it can rapidly be erased by the growth of ferromagnetic domains. We interpret the behaviour ob…
Krzakala, Ricci-Tersenghi and Zdeborova have shown recently that the random field Ising model with non-negative interactions and arbitrary external magnetic field on an arbitrary lattice does not have a static spin glass phase. In this paper we generalize the proof to a soft scalar spin version of the Ising model: the Ginzburg-Landau model with random magnetic field and random temperature-parameter. We do so by proving that the spin glass susceptibility cannot diverge unless the ferromagnetic susceptibility does.
The phase diagram of the $p$-spin-interacting spin glass model in a transverse field is investigated in the limit $p \to \infty$ under the presence of ferromagnetic bias. Using the replica method and the static approximation, we show that the phase diagram consists of four phases: Quantum paramagnetic, classical paramagnetic, ferromagnetic, and spin-glass phases. We also show that the static approximation is valid in the ferromagnetic phase in the limit $p \to \infty$ by using the large-$p$ expansion. Since the same approximation is already known to be valid in other phases, we conclude that t…
We present the full phase diagram of the spherical $2+p$ spin glass model with $p\geq 4$. The main outcome is the presence of a new phase with both properties of Full Replica Symmetry Breaking (FRSB) phases of discrete models, e.g, the Sherrington-Kirkpatrick model, and those of One Replica Symmetry Breaking (1RSB). The phase, which separates a 1RSB phase from FRSB phase, is described by an order parameter function $q(x)$ with a continuous part (FRSB) for $x<m$ and a discontinuous jump (1RSB) at $x=m$. This phase has a finite complexity which leads to different dynamic and static properties.
The search for problems where quantum adiabatic optimization might excel over classical optimization techniques has sparked a recent interest in inducing a finite-temperature spin-glass transition in quasi-planar topologies. We have performed large-scale finite-temperature Monte Carlo simulations of a two-dimensional square-lattice bimodal spin glass with next-nearest ferromagnetic interactions claimed to exhibit a finite-temperature spin-glass state for a particular relative strength of the next-nearest to nearest interactions [Phys. Rev. Lett. 76, 4616 (1996)]. Our results show that the syst…
Guided by old results on simple mode-coupling models displaying glass-glass transitions, we demonstrate, through a crude analysis of the solution with one step of replica symmetry breaking (1RSB) derived by Crisanti and Leuzzi for the spherical $s+p$ mean-field spin glass [Phys. Rev. B 73, 014412 (2006)], that the phase behavior of these systems is not yet fully understood when $s$ and $p$ are well separated. First, there seems to be a possibility of glass-glass transition scenarios in these systems. Second, we find clear indications that the 1RSB solution cannot be correct in the full glassy …
The structure of states of the perturbed p-spin spherical spin-glass is analyzed. At low enough free energy metastable states have a supersymmetric structure, while at higher free energies the supersymmetry is broken. The transition between the supersymmetric and the supersymmetry-breaking phase is triggered by a change in the stability of states.
The competition among spin glass (SG), ferromagnetism and Kondo effect has been analysed in a Kondo lattice model where the inter-site coupling $J_{ij}$ between the localized magnetic moments is given by a generalized Mattis model \cite{Mattis} which represents an interpolation between ferromagnetism and a highly disordered spin glass. Functional integral techniques with of Grassmann fields has been used to obtain the partition function. The static approximation and the replica symmetric ansatz has also been used. The solution of the problem is presented as a phase diagram temperature $T$ {\it…
True ground states are evaluated for a 2d Ising model with random near neighbor interactions and ferromagnetic second neighbor interactions (the Randomly Coupled Ferromagnet). The spin glass stiffness exponent is positive when the absolute value of the random interaction is weaker than the ferromagnetic interaction. This result demonstrates that in this parameter domain the spin glass like ordering temperature is non-zero for these systems, in strong contrast to the 2d Edwards-Anderson spin glass.
This review presents various aspects of a mean-field spin glass model known as the p-spin spherical spin glass model, which has raised a lot of interest in the study of spin glasses, and also for its possible links with a mean-field theory of structural glasses. This preprint contains no new results and is therefore not intended to be published, but its aim is to present a collection of results and formulas concerning this very rich model. It is in fact the english translation of one of the chapters of my PhD thesis (``Quelques aspects de la dynamique hors d'equilibre des verres de spin'', ``S…
A mean-field multi-spin interaction spin glass model is analyzed in the presence of a ferromagnetic coupling. The static and dynamical phase diagrams contain four phases (paramagnet, spin glass, ordinary ferromagnet and glassy ferromagnet) and exhibit reentrant behavior. The glassy ferromagnet phase has anomalous dynamical properties. The results are consistent with a nonequilibrium thermodynamics that has been proposed for glasses.
The spin glass behavior near zero temperature is a complicated matter. To get an easier access to the spin glass order parameter $Q(x)$ and, at the same time, keep track of $Q_{ab}$, its matrix aspect, and hence of the Hessian controlling stability, we investigate an expansion of the replicated free energy functional around its ``spherical'' approximation. This expansion is obtained by introducing a constraint-field and a (double) Legendre Transform expressed in terms of spin correlators and constraint-field correlators. The spherical approximation has the spin fluctuations treated with a glob…
Spin excitations of single crystal Fe0.7Al0.3 were investigated over a wide range in energy and reciprocal space with inelastic neutron scattering. In the ferromagnetic phase, propagating spin wave modes become paramagnon-like diffusive modes beyond a critical wave vector q0, indicating substantial disorder in the long-range ordered state. In the spin glass phase, spin dynamics is strongly q-dependent, suggesting remnant short-range spin correlations. Quantitative model for S(energy,q) in the ``ferromagnetic'' phase is determined.
In this work, we confront the static approximate with a exact solution in the quantum spherical p-spin interaction model (p->oo and p=2). On the one hand, this study indicates that the static approximate corresponds to exact solution in the cases p->oo and p = 2 in the classic regime. On the other, the static approximate differs from the exact solution for p=2 in the quantum regime.
We introduce a finite-connectivity ferromagnetic model with a three-spin interaction which has a crystalline (ferromagnetic) phase as well as a glass phase. The model is not frustrated, it has a ferromagnetic equilibrium phase at low temperature which is not reached dynamically in a quench from the high-temperature phase. Instead it shows a glass transition which can be studied in detail by a one step replica-symmetry broken calculation. This spin model exhibits the main properties of the structural glass transition at a solvable mean-field level.
The random-bond XY spin glass with ferromagnetic next-nearest-neighbour interactions is studied on a square lattice by Monte Carlo simulations. We find strong evidence for a finite-temperature spin glass transition at $T_c\approx 1.1$. We also give estimates for the spin glass critical exponents for different values of the strength of the nearest-neighbour interaction. Our results are consistent with universal behaviour.
The fixed point structure of the 2D 3-state random-bond Potts model with a bimodal ($\pm$J) distribution of couplings is for the first time fully determined using numerical renormalization group techniques. Apart from the pure and T=0 critical fixed points, two other non-trivial fixed points are found. One is the critical fixed point for the random-bond, but unfrustrated, ferromagnet. The other is a bicritical fixed point analogous to the bicritical Nishimori fixed point found in the random-bond frustrated Ising model. Estimates of the associated critical exponents are given for the various fi…
The finite temperature dynamics of the Dyson hierarchical classical spins models is studied via real-space renormalization rules concerning the couplings and the relaxation times. For the ferromagnetic model involving Long-Ranged coupling $J(r) \propto r^{-1-σ}$ in the region $1/2<σ<1$ where there exists a non-mean-field-like thermal Ferromagnetic-Paramagnetic transition, the RG flows are explicitly solved: the characteristic relaxation time $τ(L)$ follows the critical power-law $τ(L)\propto L^{z_c(σ)} $ at the phase transition and the activated law $\ln τ(L)\propto L^ψ $ with $ψ=1-σ$ in the f…
Aging dynamics of a reentrant ferromagnet stage-2 Cu$_{0.8}$Co$_{0.2}$Cl$_{2}$ graphite intercalation compound has been studied using DC magnetic susceptibility. This compound undergoes successive transitions at the transition temperatures $T_{c}$ ($\approx 8.7$ K) and $T_{RSG}$ ($\approx 3.3$ K). The relaxation rate $S_{ZFC}(t)$ exhibits a characteristic peak at $t_{cr}$ below $T_{c}$. The peak time $t_{cr}$ as a function of temperature $T$ shows a local maximum around 5.5 K, reflecting a frustrated nature of the ferromagnetic phase. It drastically increases with decreasing temperature below …
By means of extensive computer simulations we analyze in detail the two dimensional $\pm J$ Ising spin glass with ferromagnetic next-nearest-neighbor interactions. We found a crossover from ferromagnetic to ``spin glass'' like order both from numerical simulations and analytical arguments. We also present evidences of a second crossover from the ``spin glass'' behavior to a paramagnetic phase for the largest volume studied.
By considering the Langevin dynamics of the SK spin glass with a spherical constraint we calculate the asymptotic distance between two real replicas that evolve with the same thermal noise from different initial conditions. Despite the simplicity of the model its dynamics is known to be non trivial and presents aging phenomena. We find that the asymptotic distance between two replicas is maximal for a whole family of initial conditions that are arbitrarily close at t=0 . The asymptotic distance presents a dynamical transition at a temperature equal to the static phase transition one.
We calculate moments of free energy's finite size correction for the transition point between ferromagnetic and spin glass phases. We find, that those moments scale with the number of spins with different critical indices, characteristic for the multiscaling. This critical point corresponds to threshold of errorless coding for a gaussian noisy channel. We are give the definition of statistical complexity using this free energy approach.
We report some results on the quenched disordered Spherical multi-$p$-Spin Model in presence of ferromagnetic couplings. In particular, we present the phase diagrams of some representative cases that schematically describe, in the mean-field approximation, the behavior of most known transitions in glassy materials, including dynamic arrest in super-cooled liquids, amorphous-amorphous transitions and spin-glass transitions. A simplified notation is introduced in order to compute systems properties in terms of an effective, self-induced, field encoding the whole ferromagnetic information.
The ground-state phase diagram of an Ising spin-glass model on a random graph with an arbitrary fraction $w$ of ferromagnetic interactions is analysed in the presence of an external field. Using the replica method, and performing an analysis of stability of the replica-symmetric solution, it is shown that $w=1/2$, correponding to an unbiased spin glass, is a singular point in the phase diagram, separating a region with a spin-glass phase ($w<1/2$) from a region with spin-glass, ferromagnetic, mixed, and paramagnetic phases ($w>1/2$).
From a consideration of high temperature series expansions in ferromagnets and in spin glasses, we propose an extended scaling scaling scheme involving a set of scaling formulae which express to leading order the temperature (T) and the system size (L) dependences of thermodynamic observables over a much wider range of T than the corresponding one in the conventional scaling scheme. The extended scaling, illustrated by data on the canonical 2d ferromagnet and on the 3d binomial Ising spin glass, leads to consistency for the estimates of critical parameters obtained from scaling analyses for di…
Stage-2 Cu$_{0.93}$Co$_{0.07}$Cl$_{2}$ graphite intercalation compound magnetically behaves like a reentrant ferromagnet near the multicritical point ($c_{MCP} \approx 0.96$). It undergoes two magnetic phase transitions at $T_{RSG}$ ($= 6.64 \pm 0.05$ K) and $T_{c}$ ($= 8.62 \pm 0.05$ K). The static and dynamic nature of the ferromagnetic and reentrant spin glass phase has been studied using DC and AC magnetic susceptibility. Characteristic memory phenomena of the DC susceptibility are observed at $T_{RSG}$ and $T_{c}$. The nonlinear AC susceptibility $χ_{3}^{\prime}$ has a positive local maxi…
uch experimental and theoretical efforts have been devoted in the past twenty years to search for a genuine thermodynamic reentrant phase transition from a ferromagnetic to either a paramagnetic or spin glass phase in disordered ferromagnets. So far, no real system or theoretical model of a short-range spin glass system has been shown to convincingly display such a reentrant transition. We present here results from Migdal-Kadanoff real-space renormalization-group calculations that provide for the first time strong evidence for ferromagnetic to paramagnetic reentrance in Potts spin glasses on h…
We analyze the steady state regime of systems interpolating between spin glasses and ferromagnets under a tapping dynamics recently introduced by analogy with the dynamics of mechanically perturbed granular media. A crossover from a second order to first order ferromagnetic transition as a function of the spin coupling distribution is found. The flat measure over blocked states introduced by Edwards for granular media is used to explain this scenario. Annealed calculations of the Edwards entropy are shown to qualitatively explain the nature of the phase transitions. A Monte-Carlo construction …
We study the thermodynamic properties and the phase diagrams of a multi-spin antiferromagnetic spherical spin-glass model using the replica method. It is a two-sublattice version of the ferromagnetic spherical p-spin glass model. We consider both the replica-symmetric and the one-step replica-symmetry-breaking solutions, the latter being the most general solution for this model. We find paramagnetic, spin-glass, antiferromagnetic and mixed or glassy antiferromagnetic phases. The phase transitions are always of second order in the thermodynamic sense, but the spin-glass order parameter may unde…
Auffinger and Chen proved a variational formula for the free energy of the spherical bipartite spin glass in terms of a global minimum over the overlaps. We show that a different optimisation procedure leads to a saddle point, similar to the one achieved for models on the vertices of the hypercube.
We present the detailed analysis of the spherical s+p spin glass model with two competing interactions: among p spins and among s spins. The most interesting case is the 2+p model with p > 3 for which a very rich phase diagram occurs, including, next to the paramagnetic and the glassy phase represented by the one step replica symmetry breaking ansatz typical of the spherical p-spin model, other two amorphous phases. Transitions between two contiguous phases can also be of different kind. The model can thus serve as mean-field representation of amorphous-amorphous transitions (or transitions be…
We consider a tapping dynamics, analogous to that in experiments on granular media, on spin glasses and ferromagnets on random thin graphs. Between taps, zero temperature single spin flip dynamics takes the system to a metastable state. Tapping, corresponds to flipping simultaneously any spin with probability $p$. This dynamics leads to a stationary regime with a steady state energy $E(p)$. We analytically solve this dynamics for the one dimensional ferromagnet and $\pm J$ spin glass. Numerical simulations for spin glasses and ferromagnets of higher connectivity are carried out, in particular …
We derive the zero-temperature phase diagram of spin glass models with a generic fraction of ferromagnetic interactions on the Bethe lattice. We use the cavity method at the level of one-step replica symmetry breaking (1RSB) and we find three phases: A replica-symmetric (RS) ferromagnetic one, a magnetized spin glass one (the so-called mixed phase), and an unmagnetized spin glass one. We are able to give analytic expressions for the critical point where the RS phase becomes unstable with respect to 1RSB solutions: we also clarify the mechanism inducing such a phase transition. Finally we compa…
Some questions concerning the calculation of the number of ``physical'' (metastable) states or complexity of the spherical $p$-spin spin glass model are reviewed and examined further. Particular attention is focused on the general calculation procedure which is discussed step-by-step.
The chiral clock spin-glass model with q=5 states, with both competing ferromagnetic-antiferromagnetic and left-right chiral frustrations, is studied in d=3 spatial dimensions by renormalization-group theory. The global phase diagram is calculated in temperature, antiferromagnetic bond concentration p, random chirality strength, and right-chirality concentration c. The system has a ferromagnetic phase, a multitude of different chiral phases, a chiral spin-glass phase, and a critical (algebraically) ordered phase. The ferromagnetic and chiral phases accumulate at the disordered phase boundary a…
A continuous 3-state Potts model with an analog of spherical constraints is proposed and is shown to have an exact solution in the case of infinite-ranged interactions. "Spherical" 3-state Potts spin glass model is solved using the known properties of a large random matrix. For this model the results are identical to those obtained by the replica approach for replica symmetric solution.
In the present paper we analyze the critical properties of a quantum spherical spin glass model with short range, random interactions. Since the model allows for rigorous detailed calculations, we can show how the effective partition function calculated with help of the replica method for the spin glass fluctuating fields separates into a mean field contribution for the replica diagonal fields and a strictly short range partition function for the replica off-diagonal fields. The mean field part coincides with previous results. The short range part describes a phase transition in a Q^3-field th…
The chiral spin-glass Potts system with q=3 states is studied in d=2 and 3 spatial dimensions by renormalization-group theory and the global phase diagrams are calculated in temperature, chirality concentration p, and chirality-breaking concentration c, with determination of phase chaos and phase-boundary chaos. In d=3, the system has ferromagnetic, left-chiral, right-chiral, chiral spin-glass, and disordered phases. The phase boundaries to the ferromagnetic, left- and right-chiral phases show, differently, an unusual, fibrous patchwork (microreentrances) of all four (ferromagnetic, left-chira…
We compare the probability distributions and Binder cumulants of the overlap in the 3D Ising spin glass with those of the magnetization in the ferromagnetic 2D XY model. We analyze similarities and differences. Evidence for the existence of a phase transition in the spin glass model is obtained thanks to the crossing of the Binder cumulant. We show that the behavior of the XY model is fully compatible with the Kosterlitz-Thouless scenario. Finite size effects have to be dealt with by using great care in order to discern among two very different physical pictures that can look very similar if a…
The four-dimensional +-J random-bond Ising model is studied using ground-state calculations. System sizes up to N=6^4 spins are considered. Here it is found that the ferromagnetic-spin glass transition occurs at a critical concentration p_c=0.28(1) of the antiferromagnetic bonds, which is comparable to values found previously by high-temperature series expansions. The transition is characterized by a correlation-length exponent ν=1.0(1) and an order-parameter exponent β=0.4(1). Thus, this transition is in a different universality class from four-dimensional bond percolation, where ν=0.678(50) …
A zero temperature dynamics of Ising spin glasses and ferromagnets on random graphs of finite connectivity is considered, like granular media these systems have an extensive entropy of metastable states. We consider the problem of what energy a randomly prepared spin system falls to before becoming stuck in a metastable state. We then introduce a tapping mechanism, analogous to that of real experiments on granular media, this tapping, corresponding to flipping simultaneously any spin with probability $p$, leads to stationary regime with a steady state energy $E(p)$. We explicitly solve this pr…
The competition between spin glass, ferromagnetism and Kondo effect is analysed here in a Kondo lattice model with an inter-site random coupling $J_{ij}$ between the localized magnetic moments given by a generalization of the Mattis model which represents an interpolation between ferromagnetism and a highly disordered spin glass. Functional integral techniques with Grassmann fields have been used to obtain the partition function. The static approximation and the replica symmetric ansatz have also been used. The solution of the problem is presented as a phase diagram giving $T/{J}$ {\it versus}…
In his Comment, Krakoviack [Phys. Rev. B (2007)] finds that the phase behavior of the s+p spin-glass model is different from what proposed by Crisanti and Leuzzi [Phys. Rev. B 73, 014412 (2006)] if s and p are larger than two and are separated well enough. He proposes a trial picture, based on a one step replica symmetry breaking solution, displaying a mode-coupling-like glass-to-glass transition line ending in a A3 singularity. However, actually, the physics of these systems changes when p-s is large, the instability of which the one step replica symmetry breaking glassy phase suffers turns o…
We study analytically M-spin-flip stable states in disordered short-ranged Ising models (spin glasses and ferromagnets) in all dimensions and for all M. Our approach is primarily dynamical and is based on the convergence of a zero-temperature dynamical process with flips of lattice animals up to size M and starting from a deep quench, to a metastable limit. The results (rigorous and nonrigorous, in infinite and finite volumes) concern many aspects of metastable states: their numbers, basins of attraction, energy densities, overlaps, remanent magnetizations and relations to thermodynamic states…
The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking the free energies of these two systems, in the spirit of the equivalence of ensembles of statistical mechanics. Our analysis, combined with the previous work [4], shows that such models are replica symmetric. Lastly, we briefly discuss an application of our result to the study of the Gaussian Hopfield model.
The interactions between the dielectric polarization and the fluctuations of the strain (stress) tensor in relaxor ferroelectrics are shown to give rise to the anisotropy of the anharmonic P4-term in the Landau-type free energy, however, the harmonic P2-term is still properly described by the rigid spherical random bond--random field model. These are the essential features of the compressible spherical dipolar glass model, which is used to calculate the singularities of the specific heat near field-induced critical points. The results agree with recent high-resolution calorimetric experiments …
We investigate the ensemble inequivalence of the spherical spin glass model with nonlinear interactions of polynomial order $p$. This model is solved exactly for arbitrary $p$ and is shown to have first-order phase transitions between the paramagnetic and spin glass or ferromagnetic phases for $p \geq 5$. In the parameter region around the first-order transitions, the solutions give different results depending on the ensemble used for the analysis. In particular, we observe that the microcanonical specific heat can be negative and the phase may not be uniquely determined by the temperature.
We use record dynamics (RD), a coarse-grained description of the ubiquitous relaxation phenomenology known as "aging", as a diagnostic tool to find universal features that distinguish between the energy landscapes of Ising spin models and the ferromagnet. According to RD, a non-equilibrium system after a quench relies on fluctuations that randomly generate a sequence of irreversible record-sized events (quakes or avalanches) that allow the system to escape ever-higher barriers of meta-stable states within a complex, hierarchical energy landscape. Once these record events allow the system to ov…
We study domain-wall excitations in two-dimensional random-bond Ising spin systems on a square lattice with side length L, subject to two different continuous disorder distributions. In both cases an adjustable parameter allows to tune the disorder so as to yield a transition from a spin-glass ordered ground state to a ferromagnetic groundstate. We formulate an auxiliary graph-theoretical problem in which domain walls are given by undirected shortest paths with possibly negative distances. Due to the details of the mapping, standard shortest-path algorithms cannot be applied. To solve such sho…
Ferromagnetic order in superconductors can induce a {\em spontaneous} vortex (SV) state. For external field ${\bf H}=0$, rotational symmetry guarantees a vanishing tilt modulus of the SV solid, leading to drastically different behavior than that of a conventional, external-field-induced vortex solid. We show that quenched disorder and anharmonic effects lead to elastic moduli that are wavevector-dependent out to arbitrarily long length scales, and non-Hookean elasticity. The latter implies that for weak external fields $H$, the magnetic induction scales {\em universally} like $B(H)\sim B(0)+ c…
We present an alternate solution of a Gaussian spin-glass model with infinite ranged interactions and a global spherical constraint at zero magnetic field. The replicated spin-glass Hamiltonian is mapped onto a Coulomb gas of logarithmically interacting particles confined by a logarithmic single particle potential. The precise free energy is obtained by analyzing the Painlevé $τ^{IV} [n]$ function in the $n\to 0$ limit. The large $N$ thermodynamics exactly recovers that of Kosterlitz, Thouless and Jones \cite{ktjonesPRL}. It is hoped that the approach here can be extended to apply to systems b…
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…
The Kondo lattice model has been analyzed in the presence of a random inter-site interaction among localized spins with non zero mean Jo and standard deviation J. Following the same framework previously introduced by us, the problem is formulated in the path integral formalism where the spin operators are expressed as bilinear combinations of Grassmann fields. The static approximation and the replica symmetry ansatz have allowed us to solve the problem at a mean field level. The resulting phase diagram displays several phase transitions among a ferromagnetically ordered region,a spin glass one…
We consider the random field Ising model and show rigorously that the spin glass susceptibility at equilibrium is always bounded by the ferromagnetic susceptibility, and therefore that no spin glass phase can be present at equilibrium out of the ferromagnet critical line. When the magnetization is, however, fixed to values smaller than the equilibrium one, a glassy phase can exist, as we show explicitly on the Bethe lattice.
