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arXiv · 1906.02546

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

Valentina Apollonio·Roberto D'Autilia·Benedetto Scoppola·Elisabetta Scoppola·Alessio Troiani
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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 $q$. These measures are related to the usual Gibbs measure on $\Z^2$ and turn out to be the marginal of the Gibbs measure of a suitable Ising model on the hexagonal lattice. The inertial parameter $q$ 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.

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Valentina Apollonio, Roberto D'Autilia, Benedetto Scoppola, Elisabetta Scoppola, Alessio Troiani. 2019-06-06. Criticality of measures on 2-d Ising configurations: from square to hexagonal graphs. https://doi.org/10.1007/s10955-019-02403-3

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