Spin systems on hypercubic Bethe lattices: A Bethe-Peierls approach
Abstract
We study spin systems on Bethe lattices constructed from d-dimensional hypercubes. Although these lattices are not tree-like, and therefore closer to real cubic lattices than Bethe lattices or regular random graphs, one can still use the Bethe-Peierls method to derive exact equations for the magnetization and other thermodynamic quantities. We compute phase diagrams for ferromagnetic Ising models on hypercubic Bethe lattices with dimension d=2, 3, and 4. Our results are in good agreement with the results of the same models on d-dimensional cubic lattices, for low and high temperatures, and offer an improvement over the conventional Bethe lattice with connectivity k=2d.
Cite
@article{arxiv.1412.6362,
title = {Spin systems on hypercubic Bethe lattices: A Bethe-Peierls approach},
author = {Alexander Mozeika and Anthony CC Coolen},
journal= {arXiv preprint arXiv:1412.6362},
year = {2015}
}
Comments
Version accepted for publication by the Journal of Physics A: Mathematical and Theoretical with improved list of references and with an additional section on specific heat