A continuous analysis for the antiferromagnetic Heisenberg model on the checkerboard lattice

In this paper we investigate the antiferromagnetic Heisenberg model on the checkerboard lattice by the O(3) Non-linear Sigma Model (NLSM). The checkerboard lattice is distinguished from the antiferromagnetic square lattice (with coupling constant J) by the presence of diagonal crossing (with coupling constant J′) in half of the sites. This lattice model is the direct analogous of the three-dimensional pyrochlore lattice in a two-dimensional surface. Many effects of the three-dimensional model version, as the Quantum Order-by-Disorder, have been recently described also in the checkerboard lattice. Here we have developed the continuous version of the Heisenberg model on the checkerboard lattice and applied Renormalization Group together other techniques to analyze the both cases J < J′ and J > J′. We have therefore determined the effects of the crossing interaction J′ on the phase transitions. In addition, skyrmion solutions and their possible influences on these transitions were also considered.