On the stochastic dynamics of disordered spin models
نویسندگان
چکیده
In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in equilibrium with a thermal bath. We propose a fluctuation principle that allows us to derive fluctuation-dissipation relations for many-time correlations and linear responses. We also speculate on how these features will be modified in systems evolving slowly out of equilibrium, as finite-dimensional or dilute spinglasses. Secondly, we present a formalism that allows one to derive a series of approximated equations that determine the dynamics of disordered spin models on random (hyper) graphs.
منابع مشابه
Comparative Study of Random Matrices Capability in Uncertainty Detection of Pier’s Dynamics
Because of random nature of many dependent variables in coastal engineering, treatment of effective parameters is generally associated with uncertainty. Numerical models are often used for dynamic analysis of complex structures, including mechanical systems. Furthermore, deterministic models are not sufficient for exact anticipation of structure’s dynamic response, but probabilistic models...
متن کاملComputational Method for Fractional-Order Stochastic Delay Differential Equations
Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...
متن کاملZero-Temperature Dynamics of ± J Spin Glasses and Related Models
We study zero-temperature, stochastic Ising models σ on Z with (disordered) nearest-neighbor couplings independently chosen from a distribution μ on R and an initial spin configuration chosen uniformly at random. Given d, call μ type I (resp., type F) if, for every x in Z, σ x flips infinitely (resp., only finitely) many times as t → ∞ (with probability one) — or else mixed type M. Models of ty...
متن کاملProposing A stochastic model for spread of corona virus dynamics in Nigeria
The emergence of corona virus (COVID-19) has create a great public concern as the outbreak is still ongoing and government are taking actions such as holiday extension, travel restriction, temporary closure of public work place, borders, schools, quarantine/isolation, social distancing and so on. To mitigate the spread, we proposed and analyzed a stochastic model for the continue spread of coro...
متن کاملGriffiths Singularities in the Dynamics of Disordered Ising
We study the asymptotic behaviour of the correlation function q(t)= l N =-(Si(0) Si@>) for dilute, short-range Ising ferromagnets and spin glasses with single spin-N i-1 flip dynamics, Using an eigenfunction expansion for the time evolution operator and a variational estimate for the gap in the spectrum of this operator, we prove that, for a range of temperatures above the T, of the random syst...
متن کامل