Square-Lattice Antiferromagnet Subjected to a Magnetic Field Aligned with the Order Parameter

The thermal properties of antiferromagnetic films -- in particular, the square-lattice antiferromagnet -- subjected to an external magnetic field pointing into the direction of the staggered magnetization are explored. The effective field theory analysis of the free energy density is carried out to two-loop order. While the emphasis is on finite temperature, we also discuss the behavior of the magnetization and staggered magnetization at zero temperature. Our results imply that the staggered magnetization increases in presence of the magnetic field -- reminiscent of magnetic catalysis. Most remarkably, if staggered and magnetic field strength are kept fixed, the magnetization initially grows when temperature increases.