Spin-wave theory at constant order parameter

TL;DR

This paper develops a method to analyze low-temperature properties of quantum Heisenberg magnets using a fixed order parameter approach, incorporating spin-wave excitations and higher-order corrections.

Contribution

It introduces a 1/S expansion of the Gibbs free energy at fixed order parameter, providing a new way to study thermodynamics without requiring long-range order.

Findings

The 1/S expansion yields qualitatively correct thermodynamics at low temperatures.

Two-loop correction significantly modifies the mean-field susceptibility.

Method applies even in absence of long-range magnetic order.

Abstract

We derive the low-temperature properties of spin-S quantum Heisenberg magnets from the Gibbs free energy G(M) for fixed order parameter M. Assuming that the low-lying elementary excitations of the system are renormalized spin waves, we show that a straightforward 1/S expansion of G(M) yields qualitatively correct results for the low-temperature thermodynamics, even in the absence of long-range magnetic order. We explicitly calculate the two-loop correction to the susceptibility of the ferromagnetic Heisenberg chain and show that it quantitatively modifies the mean-field result.