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

Peter Mayer·Peter Sollich
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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.

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Peter Mayer, Peter Sollich. 2003-07-09. General Solutions for Multispin Two-Time Correlation and Response Functions in the Glauber-Ising Chain. https://doi.org/10.1088/0305-4470%2F37%2F1%2F002

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