Thermodynamics of the S=1 spin ladder as a composite S=2 chain model

TL;DR

This paper explores the thermodynamic properties of a class of S=1 spin ladder models by mapping them onto composite S=2 chains, analyzing their high-temperature behavior and comparing magnetization and specific heat to effective models.

Contribution

It introduces a mapping of S=1 spin ladders with anisotropy to composite S=2 chains and analyzes their thermodynamic properties using high-temperature expansion.

Findings

Magnetization closely matches that of effective XXZ models.

Specific heat can differ significantly from effective models depending on parameters.

High-temperature expansion provides insights into thermodynamic behavior.

Abstract

A special class of S=1 spin ladder hamiltonians, with second- neighbor exchange interactions and with anisotropies in the $z$-direction, can be mapped onto one-dimensional composite S=2 (tetrahedral S=1) models. We calculate the high temperature expansion of the Helmoltz free energy for the latter class of models, and show that their magnetization behaves closely to that of standard XXZ models with a suitable effective spin $S_{eff}$, such that $S_{eff}(1+S_{eff})=< \vec{\bf S}_i^2>$, where ${\bf S}_i$ refers to the components of spin in the composite model. It is also shown that the specific heat per site of the composite model, on the other hand, can be very different from that of the effective spin model, depending on the parameters of the hamiltonian.