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.