相关论文: Mean field behaviour of spin systems with orthogon…
We consider the dynamics of a diluted mean-field spin glass model in the aging regime. The model presents a particularly rich heterogeneous behavior. In order to catch this behavior, we perform a **spin-by-spin analysis** for a **given…
I describe a class of spin models with short--range plaquette interactions whose static equilibrium properties are trivial but which display glassy dynamics at low temperatures. These models have a dual description in terms of free defects…
Ising spin-glass systems with long-range interactions ($J(r)\sim r^{-\sigma}$) are considered. A numerical study of the critical behaviour is presented in the non-mean-field region together with an analysis of the probability distribution…
The low temperature dynamics of the two- and three-dimensional Ising spin glass model with Gaussian couplings is investigated via extensive Monte Carlo simulations. We find an algebraic decay of the remanent magnetization. For the…
We discuss the mean-field theory of spin-glass models with frustrated long-range random spin exchange. We analyze the reasons for breakdown of the simple mean-field theory of Sherrington and Kirkpatrick. We relate the replica-symmetry…
We establish a general perturbative method to prove entropic Ricci curvature bounds for interacting stochastic particle systems. We apply this method to obtain curvature bounds in several examples, namely: Glauber dynamics for a class of…
Spin glasses are models of statistical mechanics in which a large number of simple elements interact with one another in a disordered fashion. One of the fundamental results of the theory is the Parisi formula, which identifies the limit of…
Some invariances under perturbations of the spin glass phase are introduced, their proofs outlined and their consequences illustrated as factorisation rules for the overlap distribution. A comparison between the state of the art for mean…
We introduce a class of dissipative quantum spin models with local interactions and without quenched disorder that show glassy behaviour. These models are the quantum analogs of the classical facilitated spin models. Just like their…
We study the non-equilibrium relaxation of the spherical spin-glass model with p-spin interactions in the $N \rightarrow \infty$ limit. We analytically solve the asymptotics of the magnetization and the correlation and response functions…
This is a short review about recent methods and results, mostly for mean field spin glasses, based on interpolation and comparison schemes. In particular, the Parisi spontaneous replica symmetry breaking phenomenon is described in the frame…
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…
We sketch a new framework for the analysis of disordered systems, in particular mean field spin glasses, which is variational in nature and within the formalism of classical thermodynamics. For concreteness, only the Sherrington-Kirkpatrick…
In order to overcome the limitations of small system sizes in spin-glass simulations, we investigate the one-dimensional Ising spin chain with power-law interactions. The model has the advantage over traditional higher-dimensional…
The Curie-Weiss model is an exactly soluble model of ferromagnetism that allows one to study in detail the thermodynamic functions, in particular their properties in the neighbourhood of the critical temperature. In this model every…
In this article we use the Mean-Variance Model in order to measure the current market state. In our study we take the approach of detecting the overall alignment of portfolios in the spin picture. The projection to the ground-states enables…
We study the fluctuation and limiting distribution of free energy in mean-field spin glass models with Ising spins under weak external fields. We prove that at high temperature, there are three sub-regimes concerning the strength of…
The study of the normalized sum of random variables and its asymptotic behaviour has been and continues to be a central chapter in probability and statistical mechanics. When those variables are independent the central limit theorem ensures…
In this talk I review some recent developments which shed light on the main connections between structural glasses and mean-field spin glass models with a discontinuous transition. I also discuss the role of quantum fluctuations on the…
The spontaneous magnetization of a two-dimensional lattice model can be expressed in terms of the partition function $W$ of a system with fixed boundary spins and an extra weight dependent on the value of a particular central spin. For the…