相关论文: Ising spin glass models versus Ising models: an ef…

We show that, above the critical temperature, if the dimension D of a given Ising spin glass model is sufficiently high, its free energy can be effectively expressed through the free energy of a related Ising model. When, in a large sense,…

Recently, it has been shown that, when the dimension of a graph turns out to be infinite dimensional in a broad sense, the upper critical surface and the corresponding critical behavior of an arbitrary Ising spin glass model defined over…

Multiplex networks consist of a fixed set of nodes connected by several sets of edges which are generated separately and correspond to different networks ("layers"). Here, the Ising model on multiplex networks with two layers is considered,…

We discuss interfaces in spin glasses. We present new theoretical results and a numerical method to characterize overlap interfaces and the stability of the spin-glass phase in extended disordered systems. We use this definition to…

The Ising spin glass in two dimensions exhibits rich behavior with subtle differences in the scaling for different coupling distributions. We use recently developed mappings to graph-theoretic problems together with highly efficient…

We study Ising spin models on finitely connected random interaction graphs which are drawn from an ensemble in which not only the degree distribution $p(k)$ can be chosen arbitrarily, but which allows for further fine-tuning of the topology…

The Ising model on ``thin'' graphs (standard Feynman diagrams) displays several interesting properties. For ferromagnetic couplings there is a mean field phase transition at the corresponding Bethe lattice transition point. For…

It has been suggested that an information geometric view of statistical mechanics in which a metric is introduced onto the space of parameters provides an interesting alternative characterisation of the phase structure, particularly in the…

Ordering at arbitrarily high temperature - entropic order - has been argued to take place in a class of generalized Ising models parameterised by a real interaction parameter $p$ when $p\ge 1$. We give a rigorous proof of this conjecture.…

We revisit classical bounds of M. E. Fisher on the ferromagnetic Ising model, and show how to efficiently use them on an arbitrary given graph to rigorously upper-bound the partition function, magnetizations, and correlations. The results…

This paper deals with the stochastic Ising model with a temperature shrinking to zero as time goes to infinity. A generalization of the Glauber dynamics is considered, on the basis of the existence of simultaneous flips of some spins. Such…

This paper develops results for the next nearest neighbour Ising model on random graphs. Besides being an essential ingredient in classic models for frustrated systems, second neighbour interactions interactions arise naturally in several…

We consider Ising model on edge-dual of uncorrelated random networks with arbitrary degree distribution. These networks have a finite clustering in the thermodynamic limit. High and low temperature expansions of Ising model on the edge-dual…

Here is proposed a general subgraph-based method for efficiently sampling certain graphical models, typically using subgraphs of a fixed treewidth, and also a related method for finding minimum energy (ground) states. In the case of models…

In this paper, we derive the limit of experiments for one parameter Ising models on dense regular graphs. In particular, we show that the limiting experiment is Gaussian in the low temperature regime, non Gaussian in the critical regime,…

The Ising model is well-known for illustrating the fundamental characteristics of phase transitions in closed systems. In this article, we propose a generalization of the two-dimensional Ising model to open systems, considering the…

We examine the phase diagram of the $p$-interaction spin glass model in a transverse field. We consider a spherical version of the model and compare with results obtained in the Ising case. The analysis of the spherical model, with and…

Statistical spin dynamics plays a key role to understand the working principle for novel optical Ising machines. Here we propose the gauge transformations for spatial photonic Ising machine, where a single spatial phase modulator…

We consider the equilibrium dynamics of Ising spin models with multi-spin interactions on sparse random graphs (Bethe lattices). Such models undergo a mean field glass transition upon increasing the graph connectivity or lowering the…

We consider large random graphs with prescribed degrees, such as those generated by the configuration model. In the regime where the empirical degree distribution approaches a limit $\mu$ with finite mean, we establish the systematic…