Reentrant behavior of an in-plane antiferromagnet in a magnetic field.

Abstract

We introduce an model, which is an Ising cubic lattice with nearest-neighbor antiferromagnetic couplings in the $x$ and $y$ directions, and nearest-neighbor ferromagnetic couplings in the $z$ direction. The in-plane antiferromagnet in a uniform magnetic field is studied by an extended mean-field method. In this method, the lattice is divided into bundles of spins along the $z$ direction. Each bundle is composed of four columns (lines) of spins along the $z$ direction and each of them is imbedded in the mean field of its neighboring bundles. The interactions within the bundle and the mean field due to the neighbors are solved exactly using the transfer-matrix method along the $z$ direction. Within this extended mean-field calculation, the system exhibits a reentrant second-order phase boundary which separates the disordered phase from the antiferromagnetic phase. In the reentrant region, the system approaches a picture of effectively one-dimensional disordered Ising models surrounded by fully magnetized lines of spins.