Replica field theory for deterministic models (II): A non-random spin glass with glassy behavior (original) (raw)
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On a classical spin glass model
Zeitschrift f�r Physik B Condensed Matter, 1983
A simple, exactly soluble, model of a spin-glass with weakly correlated disorder is presented. It includes both randomness and frustration, but its solution can be obtained without replicas. As the temperature T is lowered, the spin-glass phase is reached via an equilibrium phase transition at T--T I. The spin-glass magnetization exhibits a distinct S-shape character, which is indicative of a field-induced transition to a state of higher magnetization above a certain threshold field. For suitable probability distributions of the exchange interactions. (a) A mixed phase is found where spin-glass and ferromagnetism coexist. (b) The zero-field susceptibility has a flat plateau for 0_<T_< T~ and a Curie-Weiss behaviour for T > T I. (c) At low temperatures the magnetic specific heat is linearly dependent on the temperature. The physical origin of the dependence upon the probability distributions is explained, and a careful analysis of the ground state structure is given.
Spinodals with Disorder: from Avalanches in Random Magnets to Glassy Dynamics
Motivated by the connection between the dynamical transition predicted by the mean-field theory of glass-forming liquids and the spinodal of an Ising model in a quenched random field (RFIM) beyond mean-field, we revisit the phenomenon of spinodals in the presence of quenched disorder and develop a complete theory for it. By working at zero temperature in the quasi-statically driven RFIM, thermal fluctuations are eliminated and one can give a rigorous content to the notion of spinodal. We show that the spinodal transition is due to the depinning and the subsequent expansion of rare droplets. We work out the critical behavior, which, in any finite dimension, is very different from the mean-field one: the characteristic length diverges exponentially and the thermodynamic quantities display very mild non-analyticities much like in a Griffith phenomenon. On the basis of our results we assess the physical content and the status of the dynamical transition predicted by the mean-field theory of glassy dynamics.
On the replica method for glassy systems
Le Journal de Physique IV, 1998
In this talk we review our theoretical understanding of spin glasses paying a particular attention to the basic physical ideas. We introduce the replica method and we describe its probabilistic consequences (we stress the recently discovered importance of stochastic stability). We show that the replica method is not restricted to systems with quenched disorder. We present the consequences on the dynamics of the system when it slows approaches equilibrium are presented: they are confirmed by large scale simulations, while we are still awaiting for a direct experimental verification.
Replica symmetry breaking and the nature of the spin glass phase
1984
Abstract A probability distribution has been proposed recently by one of us as an order parameter for spin glasses. We show that this probability depends on the particular realization of the couplings even in the thermodynamic limit, and we study its distribution. We also show that the space of states has an ultrametric topology. Résumé _ Récemment, l'un d'entre nous a proposé, comme paramètre d'ordre pour les verres de spin, une distribution de probabilité.
A Spin-Glass Model with Random Couplings
We define a frustrated spin-glass model for which the Migdal-Kadanoff renormalization group is exact. Our model has random couplings, and the renormalization group acts on these. We study the high and low temperature phases of the model, exhibit a critical fixed point (in high dimension), and show that the Edwards-Anderson parameter takes a non-zero value in the low-temperature phase.
Infinite Volume Limit and Spontaneous Replica Symmetry Breaking in Mean Field Spin Glass Models
Annales Henri Poincaré, 2003
Mean field spin glasses [1] were introduced around 30 years ago as an approximation of realistic models for disordered magnetic alloys. In what follows, we make particular reference to the well known Sherrington-Kirkpatrick (SK) model [2], but most of the results we present can be proven in greater generality. The Hamiltonian of the SK model in a magnetic field h, for a given configuration of the N Ising spins σ i = ±1, i = 1, .
Journal of Physics A: Mathematical and General, 2003
In this paper, we consider a particular aspect of the relationship between mean field and finite-dimensional spin glasses. By means of a simple interpolation method, we prove that the free energy of a class of finite dimensional spin glass models with Kac-type interactions is bounded below by that of their mean field analog. As a result, Parisi theory of replica symmetry breaking can be exploited in order to give bounds on their free energy and ground state energy. Similar results hold for diluted versions of the systems.
Spin Glass Phase Exists in the Random Weak Disorder for the Villain Model
Journal of Applied Mathematics and Physics, 2014
In this work we have studied non random Villain model by introducing simple defects to calculate degeneracies of the first excited states using Pfaffian approach through a perturbation theory. The distributions of excitations of the ground states are displayed graphically. The results are indicated that spin glass occurs in the weak disorder for the Villain model. At the concentration of defect bonds 0.03 p = , the distribution behaves in the same manner as for 0.5 p = for different sizes of lattice. The latest result of the spin glass is presented in this paper.