Molecular-field approach to the spin-Peierls transition in CuGeO_3

TL;DR

This paper develops a theoretical model for the spin-Peierls transition in CuGeO_3, mapping excitations to an effective Ising model and analyzing thermodynamic properties, aligning predictions with experimental data.

Contribution

It introduces a molecular-field approach that links soliton interactions to the transition, providing new insights into the nature of the phase change in CuGeO_3.

Findings

CuGeO_3 is close to a first-order phase transition.

The linear binding potential explains the rac{2}{3} scaling law of the triplet gap.

The model accurately predicts temperature-dependent order parameter and susceptibility.

Abstract

We present a theory for the spin-Peierls transition in CuGeO_3. We map the elementary excitations of the dimerized chain (solitons) on an effective Ising model. Inter-chain coupling (or phonons) then introduce a linear binding potential between a pair of soliton and anti-soliton, leading to a finite transition temperature. We evaluate, as a function of temperature, the order parameter, the singlet-triplet gap, the specific heat, and the susceptibility and compare with experimental data on CuGeO_3. We find that CuGeO_3 is close to a first-order phase transition. We point out, that the famous scaling law \sim\delta^{2/3} of the triplet gap is a simple consequence of the linear binding potential between pairs of solitons and anti-solitons in dimerized spin chains.