Related papers: Topics on abelian spin models and related problems
We review recent numerical progress in the study of finite dimensional strongly disordered magnetic systems like spin glasses and random field systems. In particular we report in some details results for the critical properties and the…
Random fields of scales result when the class of musical scales is thought as a set of sites, and a site can be in one of two possible states (or spins): On or Off. We present a flexible simulated annealing model that produces generic…
We present a new solution of the asymmetric two-matrix model in the large $N$ limit which only involves a saddle point analysis. The model can be interpreted as Ising in the presence of a magnetic field, on random dynamical lattices with…
Ising and Potts models are an important class of discrete probability distributions which originated from statistical physics and since then have found applications in several disciplines. Simulation from these models is a well known…
Spatial documentation is exponentially increasing given the availability of Big IoT Data, enabled by the devices miniaturization and data storage capacity. Bayesian spatial statistics is a useful statistical tool to determine the dependence…
We introduce varying spin strengths to the Ising model, a central pillar of statistical physics. With inhomogeneous physical systems in mind, but also anticipating interdisciplinary applications, we present the model on network structures…
A four part series of lectures on the connection of statistical mechanics and quantum field theory. The general principles relating statistical mechanics and the path integral formulation of quantum field theory are presented in the first…
In the past 30 years there have been extensive discoveries in the theory of integrable statistical mechanical models including the discovery of non-linear differential equations for Ising model correlation functions, the theory of random…
We study the gauge-fixing and symmetries (BRST-invariance and vector supersymmetry) of various six-dimensional topological models involving Abelian or non-Abelian 2-form potentials.
Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models,…
This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and…
On locally tree-like random graphs, we relate the random cluster model with external magnetic fields and $q\geq 2$ to Ising models with vertex-dependent external fields. The fact that one can formulate general random cluster models in terms…
We study the dynamic and metastable properties of the fully connected Ising $p$-spin model with finite number of variables. We define trapping energies, trapping times and self correlation functions and we analyse their statistical…
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…
A version of non-Abelian monopole equations is explored through dimensional reductions, with often the addition of algebraic conditions. On zero curvature spaces, spinor related extensions of integrable systems have been generated, and…
In the Ising and Potts model, random cluster representations provide a geometric interpretation to spin correlations. We discuss similar constructions for the Villain and XY models, where spins take values in the circle, as well as…
We describe various aspects of statistical mechanics defined in the complex temperature or coupling-constant plane. Using exactly solvable models, we analyse such aspects as renormalization group flows in the complex plane, the distribution…
Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models,…
We study a Gaussian Potts-Hopfield model. Whereas for Ising spins and two disorder variables per site the chaotic pair scenario is realized, we find that for q-state Potts spins [{q(q-1} \over 2]-tuples occur. Beyond the breaking of a…
We present a statistical analysis of spectra of transfer matrices of classical lattice spin models; this continues the work on the eight-vertex model of the preceding paper. We show that the statistical properties of these spectra can serve…