Representation for the Pyrochlore Lattice

TL;DR

This paper introduces a geometric representation for pyrochlore and Kagomé lattices to facilitate Monte Carlo simulations of their critical properties, using advanced algorithms and finite-size scaling analysis.

Contribution

It presents a new lattice representation for Monte Carlo simulations of frustrated magnetic systems, enabling accurate determination of critical temperatures and exponents.

Findings

Critical temperature determined for the model

Critical exponents estimated using finite-size scaling

Simulation results align with theoretical expectations

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.