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Transitions of many-particle quantum systems between distinct phases at absolute-zero temperature, known as quantum phase transitions, require an exacting treatment of particle correlations. In this work, we present a general…
In this work we use tempered fractional advection-diffusion equations to model the dispersive transport in disordered materials. A numerical method is derived to approximate the solution of such differential models and we prove that it is…
The extraordinary transition which occurs in the two-dimensional O(n) model for $n<1$ at sufficiently enhanced surface couplings is studied by conformal perturbation theory about infinite coupling and by finite-size scaling of the spectrum…
We investigate corrector estimates for the solutions of a thermoelasticity problem posed in a highly heterogeneous two-phase medium and its corresponding two-scale thermoelasticity model which was derived in an earlier paper by two-scale…
We consider numerical approximations for a phase field dendritic crystal growth model, which is a highly nonlinear system that couples the anisotropic Allen-Cahn type equation and the heat equation together. We propose two efficient,…
The classification of phases and the detection of phase transitions are central and challenging tasks in diverse fields. Within physics, it relies on the identification of order parameters and the analysis of singularities in the free…
Phase diagrams serve as a highly informative tool for materials design, encapsulating information about the phases that a material can manifest under specific conditions. In this work, we develop a method in which Bayesian inference is…
We consider a theory of a scalar one-component field $\phi$ coupled to a scalar $N$-component field $\chi$. Using large $N$ techiques we calculate the effective potential in the leading order in $1/N$. We show that this is equivalent to a…
In a previous work (Li et al. Science 364, 170) [1], we proposed a heat transfer system that preserves the anti-parity-time (APT) symmetry, and observe the rest-to-motion phase transition during the symmetry breaking. Recently, it was…
A model is developed which allows the investigation and classification of the pairing phase transition in atomic nuclei. The regions of the parameter space are discussed for which a pairing phase transition can be observed. The model…
Dimensionality is a fundamental concept in physics, which plays a hidden but crucial role in various domains, including condensed matter physics, relativity and string theory, statistical physics, etc. In quantum physics, reducing…
The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the…
In this work, physics-informed neural networks are applied to incompressible two-phase flow problems. We investigate the forward problem, where the governing equations are solved from initial and boundary conditions, as well as the inverse…
From general arguments, that are valid for spin models with sufficiently short-range interactions, we derive strong constraints on the excitation spectrum across a continuous phase transition at zero temperature between a magnetic and a…
A recent simplified transfer matrix solution of the two-dimensional Ising model on a square lattice with periodic boundary conditions is generalized to periodic-antiperiodic, antiperiodic-periodic and antiperiodic-antiperiodic boundary…
Accurately predicting nonlinear transient thermal fields in two-dimensional domains is a significant challenge in various engineering fields, where conventional analytical and numerical methods struggle to balance physical fidelity with…
The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…
Despite of simplicity of the transverse antiferromagnetic Ising model with a uniform longitudinal field, its phases and involved quntum phase transitions (QPTs) are nontrivial in comparison to its ferromagnetic counterpart. For example,…
Mappings of classical computation onto statistical mechanics models have led to remarkable successes in addressing some complex computational problems. However, such mappings display thermodynamic phase transitions that may prevent reaching…
The rapid advancement of models based on artificial intelligence demands innovative monitoring techniques which can operate in real time with low computational costs. In machine learning, especially if we consider artificial neural networks…