Representation for the Pyrochlore Lattice

Abstract

This work aims to present a representation for the Kagom\'e and pyrochlore lattices for Monte Carlo simulation and some results of the critical properties. These geometric frustrated lattices are composed of corner sharing triangles and tetrahedrons respectively. The simulation was performed with the Cluster Wollf Algorithm for the spins updates using the standard ferromagnetic Ising Model. The determination of the critical temperature and exponents was done through the Histogram Technique and the Finite-Size Scalling Theory.