Hyperfine contribution to the specific heat of the one-dimensionalXYmodel

Abstract

Recent measurements by Harrison et al. of the specific heat of praseodymium ethyl sulphate (PrES) was interpreted by them in terms of the one-dimensional electric dipolar $\mathrm{XY}$ model. However, the measured values of $\frac{C}{R}$ differ substantially from the theoretical predictions. They suggested three reasons for this discrepancy, one of which was the Pr hyperfine interaction $A{S}_{j}^{z}{I}_{j}^{z}$. In order to model the experiment, the hyperfine interaction was represented by an equivalent magnetic field ${H}^{z}$ of the same size as $A$. Using this method, they obtained a reasonable fit to the data. The purpose of this paper is to include the actual hyperfine interaction, $A{S}_{j}^{z}{I}_{j}^{z}$, in the Katsura Hamiltonian. We solve for $\frac{C}{R}$ to second order in the parameter $\frac{A}{J}$. Our results remove about half the discrepancy between experiment and theory. We attribute the remainder to random strain perturbations in the crystal.