The 1/D Expansion for Classical Magnets: Low-Dimensional Models with Magnetic Field

TL;DR

This paper develops an analytical 1/D expansion method to study the magnetization of low-dimensional classical magnets under magnetic fields, accurately capturing temperature dependence and singular behaviors at low T and H.

Contribution

It introduces a first-order 1/D expansion approach to analyze classical magnets, accurately modeling susceptibility and its singularities in low-dimensional systems.

Findings

Reproduces temperature dependence of zero-field susceptibility with good accuracy.

Describes the singular behavior of susceptibility at low temperatures and magnetic fields.

Provides analytical expressions for susceptibility limits at T→0 and H→0.

Abstract

The field-dependent magnetization m(H,T) of 1- and 2-dimensional classical magnets described by the $D$-component vector model is calculated analytically in the whole range of temperature and magnetic fields with the help of the 1/D expansion. In the 1-st order in 1/D the theory reproduces with a good accuracy the temperature dependence of the zero-field susceptibility of antiferromagnets \chi with the maximum at T \lsim |J_0|/D (J_0 is the Fourier component of the exchange interaction) and describes for the first time the singular behavior of \chi(H,T) at small temperatures and magnetic fields: \lim_{T\to 0}\lim_{H\to 0} \chi(H,T)=1/(2|J_0|)(1-1/D) and \lim_{H\to 0}\lim_{T\to 0} \chi(H,T)=1/(2|J_0|).