The internal energies of Heisenberg magnetic systems

TL;DR

This paper investigates the internal energies of quantum Heisenberg magnetic systems with arbitrary spin using Green's function methods, revealing quantum fluctuation effects near phase transitions.

Contribution

It derives new expressions for internal energies of ferromagnetic and antiferromagnetic systems considering higher order correlations and three-component magnetizations.

Findings

Neighboring spins tend to be antiparallel in FM and parallel in AFM near transition points for S<=3/2.

Quantum fluctuations significantly influence spin alignments near phase transitions.

Expressions for internal energies including three-component magnetizations are provided.

Abstract

The internal energies, including transverse and longitudinal parts, of quantum Heisenberg systems for arbitrary spin S are investigated by the double-time Green's function method. The expressions for ferromagnetic (FM) and antiferromagnetic (AFM) systems are derived when one component of magnetization is considered with the higher order longitudinal correlation functions being carefully treated. An unexpected result is that around the order and disorder transition points the neighboring spins in a FM (AFM) system are more likely longitudinally antiparallel (parallel) than parallel (antiparallel) to each other for S<=3/2 in spite of the FM (AFM) exchange between the spins. This is attributed to the strong quantum fluctuation of the systems with small S values. We also present the expressions of the internal energies of FM systems when the three-component of magnetizations are considered.