Annales de l’Institut Henri Poincaré D

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Volume 3, Issue 2, 2016, pp. 121–138
DOI: 10.4171/AIHPD/26

Published online: 2016-05-19

Bipartite dimer representation of squares of 2d-Ising correlations

Béatrice de Tilière[1]

(1) Université Pierre et Marie Curie, Paris, France

The combinatorial Bosonisation identities of [5] show that the square of 2d-Ising order and disorder correlations are equal to ± the ratio of bipartite dimer partition functions. In this self-contained paper, we give an alternative proof of these identities using the approach of [2]. Our proof is more direct and allows to see the eect of order and disorder on XOR-Ising polygon congurations.

Keywords: Bipartite dimer model, two-dimensional Ising model, correlation functions, XOR-Ising model

de Tilière Béatrice: Bipartite dimer representation of squares of 2d-Ising correlations. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 3 (2016), 121-138. doi: 10.4171/AIHPD/26