A Derivation of the Fradkin-Shenker Result From Duality: Links to Spin Systems in External Magnetic Fields and Percolation Crossovers

Details A Derivation of the Fradkin-Shenker Result From Duality: Links to Spin Systems in External Magnetic Fields and Percolation Crossovers A Derivation of the Fradkin-Shenker Result From Duality: Links to Spin Systems in External Magnetic Fields and Percolation Crossovers

2004-11-08

arxiv.org/abs/cond-mat/0411163v5

Phys.Rev. D72 (2005) 054509

Physics

Condensed Matter

Statistical Mechanics

7 pages, 7 figures

Scientific paper

10.1103/PhysRevD.72.054509

In this article, we illustrate how the qualitative phase diagram of a gauge theory coupled to matter can be directly proved and how rigorous numerical bounds may be established. Our work reaffirms the seminal result of Fradkin and Shenker from another vista. Our main ingredient is the combined use of the self-duality of the three dimensional Z2/Z2 theory and an extended Lee-Yang theorem. We comment on extensions of these ideas and firmly establish the existence of a sharp crossover line in the two dimensional Z2/Z2 theory.

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