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Various combinatorial optimization NP-hard problems can be reduced to finding the minimizer of an Ising model, which is a discrete mathematical model. It is an intellectual challenge to develop some mathematical tools or algorithms for…

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…

The $q$-neighbor Ising model is investigated on homogeneous random graphs with a fraction of edges associated randomly with antiferromagnetic exchange integrals and the remaining edges with ferromagnetic ones. It is a nonequilibrium model…

The Ising spin glass is a one-parameter exponential family model for binary data with quadratic sufficient statistic. In this paper, we show that given a single realization from this model, the maximum pseudolikelihood estimate (MPLE) of…

We show that a large collection of statistical mechanical systems with quadratically represented Hamiltonians on the complete graph can be extended to infinite exchangeable processes. This extends a known result for the ferromagnetic…

Modeling complex systems, like neural networks, simple liquids or flocks of birds, often works in reverse to textbook approaches: given data for which averages and correlations are known, we try to find the parameters of a given model…

We present analytical results for the strongly anisotropic random field Ising model, consisting of weakly interacting spin chains. We combine the mean-field treatment of interchain interactions with an analytical calculation of the average…

We construct a map between the quantum field theory of free Weyl or Majorana fermions and the probability distribution of a classical statistical ensemble for Ising spins or discrete bits. More precisely, a Grassmann functional integral…

Inspired by a continuously increasing interest in modeling and framing complex systems in a thermody- namic rationale, in this paper we continue our investigation in adapting well known techniques (originally stemmed in fields of physics…

The antiferromagnetic Ising model samples subsets of vertices of a graph with weight decaying exponentially in the number of edges induced. We study the problem of sampling from this model on the class of bipartite, regular graphs with good…

A remarkable connection has been established for antiferromagnetic 2-spin systems, including the Ising and hard-core models, showing that the computational complexity of approximating the partition function for graphs with maximum degree D…

The mean field approximation to the Ising model is a canonical variational tool that is used for analysis and inference in Ising models. We provide a simple and optimal bound for the KL error of the mean field approximation for Ising models…

Density aggregation is a central problem in machine learning, for instance when combining predictions from a Deep Ensemble. The choice of aggregation remains an open question with two commonly proposed approaches being linear pooling…

Rademacher complexity is often used to characterize the learnability of a hypothesis class and is known to be related to the class size. We leverage this observation and introduce a new technique for estimating the size of an arbitrary…

Kinetic Ising models are powerful tools for studying the non-equilibrium dynamics of complex systems. As their behavior is not tractable for large networks, many mean-field methods have been proposed for their analysis, each based on unique…

In this paper we propose a novel method to study critical systems numerically by a combined collective-mode algorithm and Renormalization Group on the lattice. This method is an improved version of MCRG in the sense that it has all the…

This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different)…

Today, the Ising model is an archetype describing collective ordering processes. And, as such, it is widely known in physics and far beyond. Less known is the fact that the thesis defended by Ernst Ising 100 years ago (in 1924) contained…

A cluster mean-field method is introduced and the applications to the Ising and Heisenberg models are demonstrated. We divide the lattice sites into clusters whose size and shape are selected so that the equivalence of all sites in a…

We consider the problem of solving TAP mean field equations by iteration for Ising model with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical…