Possible extinction of Berezinskii-Kosterlitz-Thouless transition by diagonal interactions in the checkerboard lattice

We study the thermodynamics of the classical anisotropic antiferromagnetic Heisenberg model in a checkerboard lattice. The checkerboard lattice is distinguished from the antiferromagnetic square lattice (with coupling constant J) by the presence of a diagonal crossing (coupling constant J′) in half of the sites. This lattice model is the direct analog of the three-dimensional pyrochlore lattice on a two-dimensional surface. Besides, we considered a single-ion anisotropy D that breaks the O(3) symmetry and contributes to planar spin fields. Since the model is two-dimensional endowed with an O(2) symmetry, a Berezinskii-Kosterlitz-Thouless (BKT) transition is expected to take place. We also investigated the BKT temperature as a function of the coupling constants J′ and D. The problem is developed through a continuous representation given by the O(3) Nonlinear Sigma Model (NLSM). Computer simulations were also carried out, and the results were in accordance with the analytical model.