Related papers: Modified Mean Field approximation for the Ising Mo…
We present an extension of the previously proposed mean-field renormalization method to model Hamiltonians which are characterized by more than just one type of interaction. The method rests on scaling assumptions about the magnetization of…
This paper establishes a CLT for linear statistics of the form $\langle \mathbf{q},\boldsymbol{\sigma} \rangle$ with quantitative Berry-Esseen bounds, where $\boldsymbol{\sigma}$ is an observation from an exponential family with a quadratic…
The mean-field theory for lossy nonlinear composites, described by complex and field-dependent dielectric functions, is presented. By using the spectral representation of linear composites with identical microstructure, we develop…
We study the three-dimensional system of magnetic nanoparticle dipoles randomly oriented along quenched easy axes. Directions of the magnetic momenta are described by the Ising variables which allow the momenta to flip along their random…
The sensitivity of the random field Ising model to small random perturbations of the quenched disorder is studied via exact ground states obtained with a maximum-flow algorithm. In one and two space dimensions we find a mild form of chaos,…
Motivated by a recent proposal of a Bethe approximation for the triangular Ising antiferromagnet [Phys. Rev. B {\bf 56}, 8241 (1997)], which seems to predict a disordered phase at any temperature in zero field, we analyze in some detail…
We compare dynamic mean-field and dynamic cavity as methods to describe the stationary states of dilute kinetic Ising models. We compute dynamic mean-field theory by expanding in interaction strength to third order, and compare to the exact…
We define a 2-dimensional Ising model on a triangulated sphere, $\mathbb S^2$, designed to approach the exact conformal field theory (CFT) in the continuum limit. Surprisingly, the derivation leads to a set of geometric constraints that the…
A principled method to obtain approximate solutions of general constrained integer optimization problems is introduced. The approach is based on the calculation of a mean field probability distribution for the decision variables which is…
We study inference and reconstruction of couplings in a partially observed kinetic Ising model. With hidden spins, calculating the likelihood of a sequence of observed spin configurations requires performing a trace over the configurations…
An improved unified formulation based on the effective field theory is introduced for a spin-1/2 Ising model with nearest neighbor interactions with arbitrary coordination number z. Present formulation is capable of calculating all the…
Understanding the relationship between the heterogeneous structure of complex networks and cooperative phenomena occurring on them remains a key problem in network science. Mean-field theories of spin models on networks constitute a…
We introduce a method for computing corrections to Bethe approximation for spin models on arbitrary lattices. Unlike cluster variational methods, the new approach takes into account fluctuations on all length scales. The derivation of the…
We present an improved version of our earlier work on summing the planar graphs in phi^3 field theory. The present treatment is also based on our world sheet formalism and the mean field approximation, but it makes use of no further…
Statistical modeling is a key component in the extraction of physical results from lattice field theory calculations. Although the general models used are often strongly motivated by physics, many model variations can frequently be…
The present article is based on a previous one, where a second quantized field theory on the world sheet for summing the planar graphs of phi^3 theory was developed. In this earlier work, the ground state of the model was determined using a…
A multi-chain mean-field theory is developed and applied to a two-dimensional system of weakly coupled S=1/2 Heisenberg chains. The environment of a chain C_0 is modeled by a number of neighbor chains C_d, d = +/-1,...,+/-n, with the edge…
Order-disorder phase transition of the ferromagnetic Ising model is investigated on a series of two-dimensional lattices that have negative Gaussian curvatures. Exceptional lattice sites of coordination number seven are distributed on the…
Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there have been an urge of interest in ameliorating this kind of method, mainly with…
We study a p-spin spin-glass model to understand if the finite-temperature glass transition found in the mean-field regime of p-spin models, and used to model the behavior of structural glasses, persists in the non-mean-field regime. By…