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

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.

10 pages, 1 figures, 3 tables

References in corpus (1)

• Exact solution of the spin-1/2 Ising model on the Shastry-Sutherland (orthogonal-dimer) lattice

Cited by in corpus (13)

• Ising antiferromagnet on the Archimedean lattices
• Phase transition in the majority-vote model on the Archimedean lattices
• Half-metallic ferromagnetism in layered CdOHCl induced by hole doping
• Universality of the Ising and the S=1 model on Archimedean lattices: A Monte Carlo determination
• Logarithmic divergent specific heat from high-temperature series expansions: application to the two-dimensional XXZ Heisenberg model
• Derivation of the free energy, entropy and specific heat for planar Ising models: Application to Archimedean lattices and their duals
• Minimalist Neural Networks training for phase classification in diluted-Ising models
• Dynamic approach to finite-temperature magnetic phase transitions in the extended J1- J2 model with vacancy order
• Exact solution and high temperature series expansion study of the 1/5-th depleted square lattice Ising model
• Walking on Archimedean Lattices: Insights from Bloch Band Theory
• Critical behavior of the Ising model on square-triangle tilings
• Exact critical-temperature bounds for two-dimensional Ising models
• Decorated cluster lattices: a natural framework for classical spin liquids and flat bands