Exact Curie temperature for the Ising model on Archimedean and Laves lattices

TL;DR

This paper calculates the exact Curie temperatures for the 2D Ising model on all Archimedean lattices and extends the results to Laves lattices using duality, validating some with Monte Carlo simulations.

Contribution

It provides the first exact Curie temperature calculations for all 2D Archimedean and Laves lattices, expanding the understanding of phase transitions in these systems.

Findings

Exact Curie temperatures for all Archimedean lattices.

Extension of results to Laves lattices via duality.

Comparison with Monte Carlo simulations where exact values are unknown.

Abstract

Using the Feynman-Vdovichenko combinatorial approach to the two dimensional Ising model, we determine the exact Curie temperature for all two dimensional Archimedean lattices. By means of duality, we extend our results to cover all two dimensional Laves lattices. For those lattices where the exact critical temperatures are not exactly known yet, we compare them with Monte Carlo simulations.