Unifying all classical spin models in a Lattice Gauge Theory

Details Unifying all classical spin models in a Lattice Gauge Theory Unifying all classical spin models in a Lattice Gauge Theory

2008-12-18

arxiv.org/abs/0812.3583v2

Phys.Rev.Lett.102:230502,2009

Physics

High Energy Physics

High Energy Physics - Lattice

Published version. One new figure and some minor changes

Scientific paper

10.1103/PhysRevLett.102.230502

We show that the partition function of all classical spin models, including all discrete Standard Statistical Models and all abelian discrete Lattice Gauge Theories (LGTs), can be expressed as a special instance of the partition function of the 4D Z_2 LGT. In this way, all classical spin models with apparently very different features are unified in a single complete model, and a physical relation between all models is established. As applications of this result, we present a new method to do mean field theory for abelian discrete LGTs with d>3, and we show that the computation of the partition function of the 4D Z_2 LGT is a computationally hard (#P-hard) problem. We also extend our results to abelian continuous models, where we show the approximate completeness of the 4D Z_2 LGT. All results are proven using quantum information techniques.

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