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

Abstract

We simulated the field-dependent magnetization m(H,T) and the uniform susceptibility χ(H,T) of classical Heisenberg antiferromagnets in the chain and square-lattice geometry using Monte Carlo methods. The results confirm the singular behavior of χ(H,T) at small T,H: \lim_{T \to 0}\lim_{H \to 0} χ(H,T)=1/(2J_0)(1-1/D) and \lim_{H \to 0}\lim_{T \to 0} χ(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)]