Related papers: Anomalous diffusion, Localization, Aging and Sub-a…
The experimental time scale dependence of thermodynamic relations in out-of-equilibrium systems with aging phenomena is investigated theoretically by using only aging properties of the two-time correlation functions and the generalized…
We study the Metropolis dynamics of a simple spin system without disorder, which exhibits glassy dynamics at low temperatures. We use an implementation of the algorithm of Bortz, Kalos and Lebowitz \cite{bortz}. This method turns out to be…
Machine learning (ML) methods provide advanced means for understanding inherent patterns within large and complex datasets. Here, we employ the principal component analysis (PCA) and the diffusion map (DM) techniques to evaluate the glass…
Using Monte Carlo simulations, we have studied aging phenomena in three-dimensional Gaussian Ising spin-glass model focusing on quasi-equilibrium behavior of the spin auto-correlation functions. Weak violation of the time translational…
This paper investigates the simultaneous identification of a spatially dependent potential and the initial condition in a subdiffusion model based on two terminal observations. The existence, uniqueness, and conditional stability of the…
Correlated systems at both zero and nonzero temperature are treated here from a novel angle using a functional method. This functional method is an extension of the usual effective potential method. Here, however the effective action is…
In this paper we study the asymptotic behavior of the Random-Walk Metropolis algorithm on probability densities with two different `scales', where most of the probability mass is distributed along certain key directions with the…
We analyze the dynamics of two atoms with a short-ranged pair interaction in a one-dimensional harmonic trap with time-dependent frequency. Our analysis is focused on two representative cases: (i) a sudden change of the trapping frequency…
We consider the random-field O($N$) spin model with long-range exchange interactions which decay with distance $r$ between spins as $r^{-d-\sigma}$ and/or random fields which correlate with distance $r$ as $r^{-d+\rho}$, and reexamine the…
We show that standard algorithms for anisotropic diffusion based on centered differencing (including the recent symmetric algorithm) do not preserve monotonicity. In the context of anisotropic thermal conduction, this can lead to the…
The density matrix renormalization group (DMRG) algorithm was originally designed to efficiently compute the zero temperature or ground-state properties of one dimensional strongly correlated quantum systems. The development of the…
Machine learning has become a central technique for modeling in science and engineering, either complementing or as surrogates to physics-based models. Significant efforts have recently been devoted to models capable of predicting field…
We study the spin-spin correlation function in or near the T=0 ground state of the antiferromagnetic Ising model on a triangular lattice. At zero temperature its modulation on the sublattices gives rise to two Bragg peaks in the structure…
We have conducted a thorough theoretical and numerical investigation of the electronic susceptibility, polarizability, plasmons, their damping rates, as well as the static screening in pseudospin-1 Dirac cone materials with a flat band, or…
We study the statistical mechanics of a one-dimensional log gas with general potential and arbitrary beta, the inverse of temperature, according to the method we introduced for two-dimensional Coulomb gases in [SS2]. Such ensembles…
Using Monte Carlo simulations, we study in detail the overlap distribution for individual samples for several spin-glass models including the infinite-range Sherrington-Kirkpatrick model, short-range Edwards-Anderson models in three and…
The Dyson hierarchical one-dimensional Ising model of parameter $\sigma>0$ contains long-ranged ferromagnetic couplings decaying as $1/r^{1+\sigma}$ in terms of the distance $r$. We study the stochastic dynamics near zero-temperature via…
We apply a generalization of the time-dependent DMRG to study finite temperature properties of several quantum spin chains, including the frustrated $J_1-J_2$ model. We discuss several practical issues with the method, including use of…
We study the correlation functions of quantum spin $1/2$ ladders at finite temperature, under a magnetic field, in the gapless phase at various relevant temperatures $T\neq 0$, momentum $q$ and frequencies $\omega$. We compute those…
The steady-state phase diagram of the one-dimensional reaction-diffusion model 2A -> 3A, 2A -> 0 is studied through the non-hermitian density matrix renormalization group. In the absence of single-particle diffusion the model reduces to the…