Magnetization and spin-spin energy diffusion in the XY model: a diagrammatic approach

TL;DR

This paper extends a diagrammatic cluster expansion technique to calculate time-dependent spin and energy correlation functions in the XY model, providing insights into diffusion coefficients at infinite temperature.

Contribution

It introduces a method to compute dynamic correlation functions in the XY model using diagrammatic expansions, linking theoretical calculations with experimental diffusion measurements.

Findings

Exact calculation of the first two moments of correlation functions

Estimation of diffusion coefficients consistent with experiments

Qualitative agreement with dipolar energy diffusion data

Abstract

It is shown that the diagrammatic cluster expansion technique for equilibrium averages of spin operators may be straightforwardly extended to the calculation of time-dependent correlation functions of spin operators. We use this technique to calculate exactly the first two non-vanishing moments of the spin-spin and energy-energy correlation functions of the XY model with arbitrary couplings, in the long-wavelength, infinite temperature limit appropriate for spin diffusion. These moments are then used to estimate the magnetization and spin-spin energy diffusion coefficients of the model using a phenomenological theory of Redfield. Qualitative agreement is obtained with recent experiments measuring diffusion of dipolar energy in calcium fluoride.