Related papers: The Eggbox Ising Model
The main contribution of the current study is two-fold. First, we investigate the energy landscape of the Ising and Potts models on finite two-dimensional lattices without external fields in the low temperature regime. The complete analysis…
Multidimensional potential energy landscapes (PELs) have a Gaussian distribution for the energies of the minima, but at the same time the distribution of the hyperareas for the basins of attraction surrounding the minima follows a…
We propose the Wishart planted ensemble, a class of zero-field Ising models with tunable algorithmic hardness and specifiable (or planted) ground state. The problem class arises from a simple procedure for generating a family of random…
To investigate novel aspects of pattern formation in spin systems, we use a mapping between reactive concentrations in a reaction-diffusion system and spin orientations in a dynamic multiple-spin Ising model. While pattern formation in…
We consider a stochastic process of heat conduction where energy is redistributed along a chain between nearest neighbor sites via an improper beta distribution. Similar to the well-known Kipnis-Marchioro-Presutti (KMP) model, the finite…
A one-dimensional Ising model with nearest neighbour interactions is applied to study compaction processes in granular media. An equivalent particle-hole picture is introduced, with the holes being associated to the domain walls of the…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…
We generate inherent structures, local potential-energy minima, of the "$k$-space overlap potential" in two-dimensional many-particle systems using a cooling and quenching simulation technique. The ground states associated with the…
The inverse Ising problem and its generalizations to Potts and continuous spin models have recently attracted much attention thanks to their successful applications in the statistical modeling of biological data. In the standard setting,…
This work maps deep neural networks to classical Ising spin models, allowing them to be described using statistical thermodynamics. The density of states shows that structures emerge in the weights after they have been trained --…
Interdependence is a fundamental ingredient to analyze the stability of many real-world complex systems featuring functional liasons. Yet, physical realizations of this coupling are still unknown, due to the lack of a theoretical framework…
We present detailed analytical calculations for an 1D Ising ring of arbitrary number of spin-1/2 particles, in order to reveal entanglement properties of the stationary states. We show that the ground state and specific eigenstates of the…
Motivated by the study of the metastable stochastic Ising model at subcritical temperature and in the limit of a vanishing magnetic field, we extend the notion of ($\kappa$, $\lambda$)-capacities between sets, as well as the associated…
Network data often arises via a series of structured interactions among a population of constituent elements. E-mail exchanges, for example, have a single sender followed by potentially multiple receivers. Scientific articles, on the other…
The spherical version of the Hopfield model for pattern recognition is considered in the static limit. Structures inside the patterns are modeled by Gaussian random variables that reward correlation between pairs of spins in a given…
We study a two dimensional Ising model between thermostats at different temperatures. By applying the recently introduced KQ dynamics, we show that the system reaches a steady state with coexisting phases transversal to the heat flow. The…
Pairwise models like the Ising model or the generalized Potts model have found many successful applications in fields like physics, biology, and economics. Closely connected is the problem of inverse statistical mechanics, where the goal is…
This article is divided into two parts. In the first part, we study the hierarchical phenomenon of metastability in low-temperature lattice models in the most general setting. Given an abstract dynamical system governed by a Hamiltonian…
In this article, we investigate the energy landscape and metastable behavior of the Ising and Potts models on two-dimensional square or hexagonal lattices in the low temperature regime, especially in the absence of an external magnetic…
What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems which can be solved. An example of such a system is the…