Two conditions are derived for Ising models to show non-universal critical behaviour, namely, conditions concerning (i) logarithmic singularity of the specific heat and (ii) degeneracy of the ground state. These conditions are satisfied by 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 rotational invariance.

arXiv:cond-mat/0404572Journal of Physics A Mathematical and GeneralNov 21, 199413 citations

Non-Universal Critical Behaviour of Two-Dimensional Ising Systems

Kazuhiko Minami, Masuo Suzuki

PACS number: 05.50 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. 1 § 1

Jan 1, 200412 citations