General Solutions for Multispin Two-Time Correlation and Response Functions in the Glauber-Ising Chain

TL;DR

This paper presents a new method to explicitly solve the hierarchy of equations for multispin two-time correlation and response functions in the Glauber-Ising chain, providing exact results for complex observables.

Contribution

The authors develop a novel approach to derive closed-form expressions for multispin two-time correlation and response functions in the Glauber-Ising model, including cases involving more than two spins.

Findings

Explicit solutions for multispin two-time correlation functions.

Exact results for two and four-spin correlation and response functions.

New insights into particle correlations in diffusion-limited annihilation.

Abstract

The kinetic Glauber-Ising spin chain is one of the very few exactly solvable models of non-equilibrium statistical mechanics. Nevertheless, existing solutions do not yield tractable expressions for two-time correlation and response functions of observables involving products of more than one or two spins. We use a new approach to solve explicitly the full hierarchy of differential equations for the correlation and response functions. From this general solution follow closed expressions for arbitrary multispin two-time correlation and response functions, for the case where the system is quenched from equilibrium at T_i > 0 to some arbitrary T >= 0. By way of application, we give the results for two and four-spin two-time correlation and response functions. From the standard mapping, these also imply new exact results for two-time particle correlation and response functions in one-dimensional diffusion limited annihilation.