Solvable Kinetic Gaussian Model in External Field

TL;DR

This paper analyzes the dynamic behavior of the Gaussian spin model under a periodic external field, deriving exact solutions for local magnetization and correlations, and exploring how external field parameters influence system dynamics.

Contribution

It provides an exact analytical treatment of the kinetic Gaussian model in an external field, including derivation of dynamic equations and analysis of critical dynamical properties.

Findings

Time evolution depends on external field frequency and wave vector.

Exact solutions for local magnetization and pair correlation functions.

System's dynamical response varies with external field parameters.

Abstract

In this paper, the single-spin transition dynamics is used to investigate the kinetic Gaussian model in a periodic external field. We first derive the fundamental dynamic equations, and then treat an isotropic d-dimensional hypercubic lattice Gaussian spin system with Fourier's transformation method. We obtain exactly the local magnetization and the equal-time pair correlation function. The critical characteristics of the dynamical, the complex susceptibility, and the dynamical response are discussed. The results show that the time evolution of the dynamical quantities and the dynamical responses of the system strongly depend on the frequency and the wave vector of the external field.