Journal article
Duality in long‐range Ising ferromagnets
Journal of mathematical physics, Vol.35(2), pp.769-779
02/1994
DOI: 10.1063/1.530610
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.
Details
- Title: Subtitle
- Duality in long‐range Ising ferromagnets
- Creators
- Yannick Meurice - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Journal of mathematical physics, Vol.35(2), pp.769-779
- DOI
- 10.1063/1.530610
- ISSN
- 0022-2488
- eISSN
- 1089-7658
- Number of pages
- 11
- Language
- English
- Date published
- 02/1994
- Academic Unit
- Physics and Astronomy
- Record Identifier
- 9984200051802771
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