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Duality in long‐range Ising ferromagnets
Journal article   Peer reviewed

Duality in long‐range Ising ferromagnets

Yannick Meurice
Journal of mathematical physics, Vol.35(2), pp.769-779
02/1994
DOI: 10.1063/1.530610
url
https://arxiv.org/pdf/hep-lat/9208015View
Open Access

Abstract

It is proved that for a system of spins σ i =±1 having an interaction energy −∑K ij σ i σ j with all the K ij strictly positive, one can construct a dual formulation by associating a dual spin S ijk =±1 to each triplet of distinct sites i, j, and k. The dual interaction energy reads −∑(ij) D ij Π k≠i,j S ijk with tanh(K ij )=exp(−2D ij ), and it is invariant under local symmetries. The gauge‐fixing procedure, identities relating averages of order and disorder variables, and representations of various quantities as integrals over Grassmann variables are discussed. The relevance of these results for Polyakov’s approach of the 3‐D Ising model is briefly discussed.
LATTICE FIELD THEORY SPIN SYSTEMS FERROMAGNETISM ORDER PARAMETERS DUALITY ISING MODEL PARTITION FUNCTIONS GAUGE INVARIANCE ORDER−DISORDER MODEL LATTICE DYNAMICS RENORMALIZATION

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