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Duality in generalized Ising models · Around

2014

Duality in generalized Ising models

Wegner, Franz J.

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This paper rests to a large extend on a paper I wrote some time ago on 'Duality in generalized Ising models and phase transitions without local order parameter'.

It deals with Ising models with interactions containing products of more than two spins.
In contrast to the old paper I will first give examples before I come to the general statements.
Of particular interest is a gauge invariant Ising model in four dimensions.

Built on

M. Creutz, L. Jacobs, and C. Rebbi, Monte Carlo study of Abelian lattice gauge theories
1915
Earlier work this paper cites.
H.A. Kramers and G.H. Wannier, Statistics of the two-dimensional ferromagnet. Parts I and II
1941
Earlier work this paper cites.
L. Onsager, Crystal Statistics. I. A two-dimensional model with an order-disorder transition
1944
Earlier work this paper cites.
G.H. Wannier, The statistical problem in cooperative phenomena
1945
Earlier work this paper cites.
L.P. Kadanoff and H. Ceva, Determination of an operator algebra for the two-dimensional Ising model
1971
Earlier work this paper cites.
F.J. Wegner, Duality in generalized Ising models and phase transitions without local order parameter
1971
Earlier work this paper cites.

Similar

F.J. Wegner, A transformation including the weak-graph theorem and the duality transformation
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T. Weiland, A discretization model for the solution of Maxwell’s equations for six-component fields
1977
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C.P. Korthals Altes, Duality for Z(N) gauge theories
1978
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T. Yoneya, Z(N) topological excitations in Yang-Mills theories: duality and confinement
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Cited alongside, same era.

Then

M. Creutz, L. Jacobs, and C. Rebbi, Experiments with a gauge-invariant Ising system
1979
Later among the works it cites.
C. Rebbi, Lattice gauge theories and Monte Carlo simulations
1983
Later among the works it cites.
C. Itzykson, J.-M. Drouffe, Statistical field theory
1989
Later among the works it cites.
K.G. Wilson, The origin of lattice gauge theory
2005
Later among the works it cites.
R. Balian, J.-M. Drouffe, and C. Itzykson, Gauge fields on a lattice. II. Gauge-invariant Ising model
2098
Closest in time.

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