Logarithmic divergent specific heat from high-temperature series expansions: application to the two-dimensional XXZ Heisenberg model

TL;DR

This paper introduces an interpolation method for analyzing the specific heat near phase transitions with logarithmic singularities, validated on known models and applied to the XXZ Heisenberg model.

Contribution

The paper develops a new interpolation technique that accurately captures logarithmic divergences in specific heat at phase transitions, applicable to complex quantum models.

Findings

Accurate interpolation of specific heat in models with logarithmic singularities.

Excellent agreement with exact solutions for Ising models on various lattices.

Application of the method to the XXZ Heisenberg model where no exact results exist.

Abstract

We present an interpolation method for the specific heat $c_v(T)$, when there is a phase transition with a logarithmic singularity in $c_v$ at a critical temperature $T=T_c$. The method uses the fact that $c_v$ is constrained both by its high temperature series expansion, and just above $T_c$ by the type of singularity. We test our method on the ferro and antiferromagnetic Ising model on the two-dimensional square, triangular, honeycomb, and kagome lattices, where we find an excellent agreement with the exact solutions. We then explore the XXZ Heisenberg model, for which no exact results are available.