The Ising model for the bcc, fcc and diamond lattices: A comparison

Abstract

A large-scale Monte Carlo simulation study of the Ising model for the simple cubic lattice was recently performed by us. In this paper, we complement that study with the bcc, fcc and diamond lattices. Both the canonical and microcanonical ensembles are employed. We give estimates of the critical temperature and also other quantities in the critical region. An analysis of the critical behaviour points to distinct high- and low-temperature exponents, especially for the specific heat, as was also obtained for the simple cubic lattice, although the agreement is good between the different lattices. The source of this discrepancy is briefly discussed.

Keywords:

• Ising model
• phase transition
• scaling

Acknowledgements

This research was conducted using the resources of the High Performance Computing Center North (HPC2N) and the Center for Parallel Computers (PDC). The research was financed by the Swedish Research Council (VR) which we would like to thank. One of the authors (AR) would like to thank James L. Smith for his continuous support over the years.