Exact Solution of an Irreversible One-Dimensional Model with Fully Biased Spin Exchanges

TL;DR

This paper presents an exact solution for a one-dimensional irreversible spin exchange model with fully biased dynamics, highlighting the impact of initial conditions and suggesting different critical behavior from isotropic models.

Contribution

It provides an exact analytical solution for a specific case of an irreversible spin exchange model with fully biased rates, a scenario previously unexplored.

Findings

Exact solution for the case when one rate is zero

Strong dependence of dynamics on initial conditions

Different dynamical critical exponent from isotropic models

Abstract

We introduce a model with conserved dynamics, where nearest neighbor pairs of spins $\uparrow \downarrow (\downarrow \uparrow)$ can exchange to assume the configuration $\downarrow \uparrow (\uparrow \downarrow)$, with rate $\beta (\alpha)$, through energy decreasing moves only. We report exact solution for the case when one of the rates, $\alpha$ or $\beta$, is zero. The irreversibility of such dynamics results in strong dependence on the initial conditions. Domain wall arguments suggest that for more general models with steady states the dynamical critical exponent for the anisotropic spin exchange is different from the isotropic value.