Uniform susceptibility of classical antiferromagnets in one and two dimensions in a magnetic field

TL;DR

This study uses Monte Carlo simulations to analyze the magnetic susceptibility of classical antiferromagnets in one and two dimensions, confirming singular behavior at low temperatures and fields, and validating theoretical predictions.

Contribution

It provides numerical confirmation of the singular susceptibility behavior in classical antiferromagnets and compares results with theoretical 1/D expansion predictions.

Findings

Susceptibility diverges at low T and H as predicted.

Good agreement with 1/D expansion results across various conditions.

Identifies the order of limits affecting susceptibility behavior.

Abstract

We simulated the field-dependent magnetization m(H,T) and the uniform susceptibility \chi(H,T) of classical Heisenberg antiferromagnets in the chain and square-lattice geometry using Monte Carlo methods. The results confirm the singular behavior of \chi(H,T) at small T,H: \lim_{T \to 0}\lim_{H \to 0} \chi(H,T)=1/(2J_0)(1-1/D) and \lim_{H \to 0}\lim_{T \to 0} \chi(H,T)=1/(2J_0), where D=3 is the number of spin components, J_0=zJ, and z is the number of nearest neighbors. A good agreement is achieved in a wide range of temperatures T and magnetic fields H with the first-order 1/D expansion results [D. A. Garanin, J. Stat. Phys. 83, 907 (1996)]