# Interpolation between low and high temperatures of the specific heat for spin systems

## TL;DR

This paper develops and compares interpolation methods that combine high and low temperature data to accurately approximate the specific heat of spin systems across all temperatures, revealing features like low-temperature maxima.

## Contribution

It introduces two improved variants of the entropy method for gapped systems and demonstrates their effectiveness on quantum and classical spin systems.

## Key findings

- Interpolation detects low-temperature maxima in specific heat.
- Second variant, Log Z method, performs well on various spin systems.
- Methods work for both quantum and classical spin models.

## Abstract

The high temperature expansion (HTE) of the specific heat of a spin system fails at low temperatures, even if it is combined with a Pad\'e approximation. On the other hand we often have information about the low temperature asymptotics (LTA) of the system. Interpolation methods combine both kind of information, HTE and LTA, in order to obtain an approximation of the specific heat that holds for the whole temperature range. Here we revisit the entropy method that has been previously published and propose two variants that better cope with problems of the entropy method for gapped systems. We compare all three methods applied to the antiferromagnetic Haldane spin-one chain and especially apply the second variant, called Log Z method, to the cuboctahedron for different spin quantum numbers. In particular, we demonstrate that the interpolation method is able to detect an extra low-temperature maximum in the specific heat that may appear if a separation of two energy scales is present in the considered system. Finally we illustrate how interpolation also works for classical spin systems.