Related papers: Spin glasses and Stein's method

We discuss the utility of analytical and numerical investigation of spin models, in particular spin glasses, on ordinary ``thin'' random graphs (in effect Feynman diagrams) using methods borrowed from the ``fat'' graphs of two dimensional…

This paper constitutes the second part of a two-paper series devoted to the systematic study of vector spin glass models whose energy function involves a spin glass part and a general Mattis interaction part. In this paper, we focus on…

We identify a special class of multi-species spin glass models: ones in which the species proportions serve to ''balance'' out the interaction strengths. For this class, we prove a free energy lower bound that does not require any convexity…

Stein's method is applied to obtain a general Cramer-type moderate deviation result for dependent random variables whose dependence is defined in terms of a Stein identity. A corollary for zero-bias coupling is deduced. The result is also…

This work presents the first systematic development of Stein's method for matrix distributions. We establish the basic essential ingredients of Stein's method for matrix normal approximation: we derive a generator-based Stein identity from…

We show several calculations to identify the critical point in the ground state in random spin systems including spin glasses on the basis of the duality analysis. The duality analysis is a profound method to obtain the precise location of…

In this talk I will show that usual spin glasses are a peculiar kind of Abelian gauge theory. I will shortly review the techniques used to study them. At the end I will consider more general models (e.g. spin glasses based on non Abelian…

A new Monte Carlo algorithm for 2-dimensional spin glasses is presented. The use of clusters makes possible global updates and leads to a gain in speed of several orders of magnitude. As an example, we study the 2-dimensional +/-J…

We investigate numerically disorder chaos in spin glasses, i.e. the sensitivity of the ground state to small changes of the random couplings. Our study focuses on the Edwards-Anderson model in d=1,2,3 and in mean-field. We find that in all…

We investigate the L\'evy glass, a mean-field spin glass model with power-law distributed couplings characterized by a divergent second moment. By combining extensively many small couplings with a spare random backbone of strong bonds the…

We obtain rates of convergence in limit theorems of partial sums $S_n$ for certain sequences of dependent, identically distributed random variables, which arise naturally in statistical mechanics, in particular, in the context of the…

We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…

Exploiting the azimuthal angle dependence of the density matrices we construct observables that directly measure the spin of a heavy unstable particle. A novelty of the approach is that the analysis of the azimuthal angle dependence in a…

We provide an overview of some recent techniques involving the Malliavin calculus of variations and the so-called ``Stein's method'' for the Gaussian approximations of probability distributions. Special attention is devoted to establishing…

We consider the Sherrington-Kirkpatrick model of spin glasses with ferromagnetically biased couplings. For a specific choice of the couplings mean, the resulting Gibbs measure is equivalent to the Bayesian posterior for a high-dimensional…

This paper concerns the development of Stein's method for chi-square approximation and its application to problems in statistics. New bounds for the derivatives of the solution of the gamma Stein equation are obtained. These bounds involve…

Glass transition where viscosity of liquids increases dramatically upon decrease of temperature without any major change in structural properties, remains one of the most challenging problems in condensed matter physics (Cavagna, 2009;…

We extend Stein's method to include independence with respect to an auxiliary random variable, for any law for which a Stein characterization does exist. This extends the current literature on the problem. Using tools from the Malliavin…

The recently proposed strategy for studying the equilibrium thermodynamics of the glass phase using a molecular liquid is reviewed and tested in details on the solvable case of the $p$-spin model. We derive the general phase diagram, and…

We consider the Ising spin glass for the arbitrary spin S with the short- ranged interaction using the Bethe- Peierls approximation previously formulated by Serva and Paladin for the same system but limited to S=1/2. Results obtained by us…