English

Criticality of measures on 2-d Ising configurations: from square to hexagonal graphs

Mathematical Physics 2020-01-08 v1 math.MP Probability

Abstract

On the space of Ising configurations on the 2-d square lattice, we consider a family of non Gibbsian measures introduced by using a pair Hamiltonian, depending on an additional inertial parameter qq. These measures are related to the usual Gibbs measure on Z2\Z^2 and turn out to be the marginal of the Gibbs measure of a suitable Ising model on the hexagonal lattice. The inertial parameter qq tunes the geometry of the system. The critical behaviour and the decay of correlation functions of these measures are studied thanks to relation with the Random Cluster model.

Keywords

Cite

@article{arxiv.1906.02546,
  title  = {Criticality of measures on 2-d Ising configurations: from square to hexagonal graphs},
  author = {Valentina Apollonio and Roberto D'Autilia and Benedetto Scoppola and Elisabetta Scoppola and Alessio Troiani},
  journal= {arXiv preprint arXiv:1906.02546},
  year   = {2020}
}