Related papers: How to Compute Loop Corrections to Bethe Approxima…
Improving perturbation theory via a variational optimization has generally produced in higher orders an embarrassingly large set of solutions, most of them unphysical (complex). We introduce an extension of the optimized perturbation method…
The sample-to-sample fluctuations of the free energy in finite-dimensional Ising spin glasses are calculated, using the replica method, from higher order terms in the replica number $n$. It is shown that the Parisi symmetry breaking scheme…
We consider $t$-Lee-error-correcting codes of length $n$ over the residue ring $\mathbb{Z}_m := \mathbb{Z}/m\mathbb{Z}$ and determine upper and lower bounds on the number of $t$-Lee-error-correcting codes. We use two different methods,…
We propose a generalization of the cavity method to quantum spin glasses on fixed connectivity lattices. Our work is motivated by the recent refinements of the classical technique and its potential application to quantum computational…
Bethe Lattice Spin Glasses (BLSG) are models with finite connectivity which undergo a Replica Symmetry Breaking (RSB) phase transition in field, even at zero temperature. The order parameter describing this phase is a function related to…
We first present an empirical study of the Belief Propagation (BP) algorithm, when run on the random field Ising model defined on random regular graphs in the zero temperature limit. We introduce the notion of maximal solutions for the BP…
A theory for the complexity of the Bethe lattice spin-glass is developed applying to the cavity-method scheme of Mezard and Parisi the results recently obtained in the context of the Sherrington-Kirkpatrick model. The crucial ingredient is…
The Bethe approximation is a successful method for approximating partition functions of probabilistic models associated with a graph. Recently, Chertkov and Chernyak derived an interesting formula called Loop Series Expansion, which is an…
We compute the Gaussian-fluctuation corrections to the saddle-point Schwinger-boson results using collective coordinate methods. Concrete application to investigate the frustrated J1-J2 antiferromagnet on the square lattice shows that,…
A way to lower computational cost in large scale inverse problems and problems depending on poorly known model parameters is to replace the detailed model by an approximate one. Inverse problems are typically ill-posed, and the model…
A fluctuating non-ideal fluid at its critical point is simulated with the Lattice Boltzmann method. It is demonstrated that the method, employing a Ginzburg-Landau free energy functional, correctly reproduces the static critical behavior…
In this article we propose a simple approach for the precision calculation of Bethe logarithm. The leading contributions are obtained using specific operators, while the remaining terms are eliminated by adjusting the parameter $\lambda$.…
A general numerical method is presented to locate the partition function zeros in the complex beta plane for large lattice sizes. We apply this method to the 2D Ising model and results are reported for square lattice sizes up tp L=64. We…
The cluster variation - Pade` approximant method is a recently proposed tool, based on the extrapolation of low/high temperature results obtained with the cluster variation method, for the determination of critical parameters in Ising-like…
We study classical Ising spin-$\frac{1}{2}$ models on the 2D square lattice with ferromagnetic or antiferromagnetic nearest-neighbor interactions, under the effect of a pure imaginary magnetic field. The complex Boltzmann weights of spin…
We study numerically the scaling correction to the internal energy per spin as a function of system size and temperature in a variety of Ising and vector spin glasses. From a standard scaling analysis we estimate the effective size…
The average ground state energies for spin glasses on Bethe lattices of connectivities r=3,...,15 are studied numerically for a Gaussian bond distribution. The Extremal Optimization heuristic is employed which provides high-quality…
In a series of papers we have found identical behaviour for various spin models on thin random graphs - Feynman diagrams - and the corresponding Bethe lattices. In this note we observe that in all cases the ratios of various saddle point…
We prove that the scaling limits of spin fluctuations in four-dimensional Ising-type models with nearest-neighbor ferromagnetic interaction at or near the critical point are Gaussian. A similar statement is proven for the $\lambda \phi^4$…
Mixed-spin Ising model on a decorated Bethe lattice is rigorously solved by combining the decoration-iteration transformation with the method of exact recursion relations. Exact results for critical lines, compensation temperatures, total…