Related papers: Image restoration using the chiral Potts spin-glas…
We investigate static and dynamic properties of gray-scale image restoration (GSIR) by making use of the Q-Ising spin glass model, whose ladder symmetry allows to take in account the distance between two spins. We thus give an explicit…
We develop a statistical-mechanical formulation for image restoration and error-correcting codes. These problems are shown to be equivalent to the Ising spin glass with ferromagnetic bias under random external fields. We prove that the…
A continuous 3-state Potts model with an analog of spherical constraints is proposed and is shown to have an exact solution in the case of infinite-ranged interactions. "Spherical" 3-state Potts spin glass model is solved using the known…
We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all…
Spin glasses featured by frustrated interactions and metastable states have important applications in chemistry, material sciences and artificial neural networks. However, the solution of the spin glass models is hindered by the…
An analysis is made of various methods of phenomenological renormalization based on finite-size scaling equations for inverse correlation lengths, the singular part of the free energy density, and their derivatives. The analysis is made…
Implicit neural representations (INRs) have emerged as a powerful tool for solving inverse problems in computer vision and computational imaging. INRs represent images as continuous domain functions realized by a neural network taking…
The chiral spin-glass Potts system with q=3 states is studied in d=2 and 3 spatial dimensions by renormalization-group theory and the global phase diagrams are calculated in temperature, chirality concentration p, and chirality-breaking…
This work is concerned with the theory of Graphical Representation for the Ising and Potts Models over general lattices with non-translation invariant external field. We explicitly describe in terms of the Random Cluster Representation the…
Reconstruction of images corrupted by noise is an important problem in Image Analysis. In the standard Bayesian approach the unknown original image is assumed to be a realization of a Markov random field on a finite two dimensional finite…
Implicit neural representations (INRs) have emerged as a powerful tool for solving inverse problems in computer vision and computational imaging. INRs represent images as continuous domain functions realized by a neural network taking…
We report on the restoration of gray-scale image when it is decomposed into a binary form before transmission. We assume that a gray-scale image expressed by a set of Q-Ising spins is first decomposed into an expression using Ising (binary)…
Optical simulators for the Ising model have demonstrated great promise for solving challenging problems in physics and beyond. Here, we develop a spatial optical simulator for a variety of classical statistical systems, including the clock,…
We present and solve the Replica Symmetric equations in the context of the Replica Cluster Variational Method for the 2D random bond Ising model (including the 2D Edwards-Anderson spin glass model). First we solve a linearized version of…
In this paper we study the large-N limits of the integrable N-state chiral Potts model. Three chiral solutions of the star-triangle equations are derived, with states taken from all integers, or from a finite or infinite real interval.…
We solve the q-state Potts model with anti-ferromagnetic interactions on large random lattices of finite coordination. Due to the frustration induced by the large loops and to the local tree-like structure of the lattice this model behaves…
Ising machines are emerging as a powerful physical alternative to digital processors for solving combinatorial optimization problems. Among them, spatial photonic Ising machines (SPIMs) offer compact, room-temperature hardware with…
Spin-glass and chiral-glass orderings of a three-dimensional isotropic Heisenberg spin glass are studied both by equilibrium and off-equilibrium Monte Carlo simulations with emphasis on their dynamical aspects. The model is found to exhibit…
Extensive equilibrium Monte Carlo simulations are performed for a three-dimensional Heisenberg spin glass with the nearest-neighbor Gaussian coupling to investigate its spin-glass and chiral-glass orderings. The occurrence of a…
Spin-glass and chiral-glass orderings in three-dimensional Heisenberg spin glasses are studied both by equilibrium and off-equilibrium Monte Carlo simulations. Fully isotropic model is found to exhibit a finite-temperature chiral-glass…