Duality in Generalized Ising Models and Phase Transitions without Local Order Parameters
Abstract
It is shown that any Ising model with positive coupling constants is related to another Ising model by a duality transformation. We define a class of Ising models M_{dn} on ddimensional lattices characterized by a number n = 1, 2, …, d (n = 1 corresponds to the Ising model with twospin interaction). These models are related by two duality transformations. The models with 1 < n < d exhibit a phase transition without local order parameter. A nonanalyticity in the specific heat and a different qualitative behavior of certain spin correlation functions in the low and the high temperature phases indicate the existence of a phase transition. The Hamiltonian of the simple cubic dual model contains products of four Ising spin operators. Applying a star square transformation, one obtains an Ising model with competing interactions exhibiting a singularity in the specific heat but no longrange order of the spins in the low temperature phase.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 October 1971
 DOI:
 10.1063/1.1665530
 Bibcode:
 1971JMP....12.2259W