Non-Universal Critical Behaviour of Two-Dimensional Ising Systems

Abstract

Two conditions are derived for Ising models to show non-universal critical behaviour, namely conditions concerning 1) logarithmic singularity of the specific heat and 2) degeneracy of the ground state. These conditions are satisfied with the eight-vertex model, the Ashkin-Teller model, some Ising models with short- or long-range interactions and even Ising systems without the translational or the rotational invariance.

17 pages

Cited by in corpus (5)

• Monte Carlo studies of the square Ising model with next-nearest-neighbor interactions
• Quenched bond randomness in marginal and non-marginal Ising spin models in 2D
• First-order transition features of the triangular Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions
• Spin-1/2 Ising-Heisenberg model with the pair XYZ Heisenberg interaction and quartic Ising interactions as the exactly soluble zero-field eight-vertex model
• Wang-Landau study of the random bond square Ising model with nearest- and next-nearest-neighbor interactions