Spin systems on hypercubic Bethe lattices: A Bethe-Peierls approach

Alexander Mozeika; Anthony CC Coolen

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arXiv · 1412.6362

Spin systems on hypercubic Bethe lattices: A Bethe-Peierls approach

Alexander Mozeika·Anthony CC Coolen

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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.

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Alexander Mozeika, Anthony CC Coolen. 2014-12-19. Spin systems on hypercubic Bethe lattices: A Bethe-Peierls approach. https://arxiv.org/abs/1412.6362

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