Related papers: Machine learning the Ising transition: A compariso…
A model in statistical mechanics, characterised by the corresponding Gibbs measure, is a subset of the totality of probability distributions on the phase space. The shape of this subset, i.e., the geometry, then plays an important role in…
A two-temperature Ising-Schelling model is introduced and studied for describing human segregation. The self-organized Ising model with Glauber kinetics simulated by M\"uller et al. exhibits a phase transition between segregated and mixed…
Integro-partial differential equations occur in many contexts in mathematical physics. Typical examples include time-dependent diffusion equations containing a parameter (e.g., the temperature) that depends on integrals of the unknown…
Transfer-matrix methods are used, in conjunction with finite-size scaling and conformal invariance concepts, to generate an accurate phase diagram for a two-dimensional square-lattice Ising spin-1/2 magnet, with couplings which are positive…
Employing a deep convolutional neural network (deep CNN) trained on spin configurations of the 2D Ising model and the temperatures, we examine whether the deep CNN can detect the phase transition of the 2D $q$-state Potts model. To this…
Critical behavior of three-dimensional classical frustrated antiferromagnets with a collinear spin ordering and with an additional twofold degeneracy of the ground state is studied. We consider two lattice models, whose continuous limit…
We consider the phase separation problem for the one--dimensional ferromagnetic Ising model with long--range two--body interaction, $J(n)=n^{-2+\a}$ where $n\in \N$ denotes the distance of the two spins and $ \alpha \in ]0,\a_+[$ with…
We study the Ising model under a time-varying, but spatially homogeneous, Gaussian random magnetic field. In the Monte Carlo simulations, we go beyond the standard analysis of the order parameter by measuring the magnetization probability…
The two dimensional ferromagnetic Ising model in the presence of a propagating magnetic field wave (with well defined frequency and wavelength) is studied by Mone Carlo simulation. This study differs from all of the earlier studies done so…
This paper presents the investigation of convolutional neural network (CNN) prediction successfully recognizing the temperature of the non-equilibrium phases and phase transitions in two-dimensional (2D) Ising spins on square-lattice. The…
The comparison between discriminative and generative classifiers has intrigued researchers since Efron's seminal analysis of logistic regression versus discriminant analysis. While early theoretical work established that generative…
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…
Phase segregation, the process by which the components of a binary mixture spontaneously separate, is a key process in the evolution and design of many chemical, mechanical, and biological systems. In this work, we present a data-driven…
A systematic study of both classical and quantum geometric frustrated Ising models with a competing ordering mechanism is reported in this paper. The ordering comes in the classical case from a coupling of 2D layers and in the quantum model…
In the study of phase transitions a very few models are accessible to exact solution. In the most cases analytical simplifications have to be done or some numerical technique has to be used to get insight about their critical properties.…
We revisit the one-dimensional ferromagnetic Ising spin-chain with a finite number of spins and periodic boundaries and derive analytically and verify numerically its various stationary and dynamical properties at different temperatures. In…
Quantum phase transitions in many-body systems are fundamentally characterized by complex correlation structures, which pose computational challenges for conventional methods in large systems. To address this, we propose a hybrid…
We investigated the Ising model on a square lattice with ferro and antiferromagnetic interactions modulated by the quasiperiodic Octonacci sequence in both directions of the lattice. We have applied the Replica Exchange Monte Carlo…
A phase transition indicates a sudden change in the properties of a large system. For temperature-driven phase transitions this is related to non-analytic behavior of the free energy density at the critical temperature: The knowledge of the…
Neural networks possess formidable representational power, rendering them invaluable in solving complex quantum many-body systems. While they excel at analyzing static solutions, nonequilibrium processes, including critical dynamics during…