Tunneling and the Spectrum of the Potts Model

Details Tunneling and the Spectrum of the Potts Model Tunneling and the Spectrum of the Potts Model

1992-06-22

arxiv.org/abs/hep-lat/9206017v1

Phys.Rev.D47:4091-4101,1993

Physics

High Energy Physics

High Energy Physics - Lattice

26 pages plus 13 Postscript figures (Axis versions also provided), UU-HEP-92/4

Scientific paper

10.1103/PhysRevD.47.4091

The three-dimensional, three-state Potts model is studied as a paradigm for high temperature quantum chromodynamics. In a high statistics numerical simulation using a Swendson-Wang algorithm, we study cubic lattices of dimension as large as $64^3$ and measure correlation functions on long lattices of dimension $20^2\times 120$ and $30^2\times 120$. These correlations are controlled by the spectrum of the transfer matrix. This spectrum is studied in the vicinity of the phase transition. The analysis classifies the spectral levels according to an underlying $S_3$ symmetry. Near the phase transition the spectrum agrees nicely with a simple four-component hamiltonian model. In the context of this model, we find that low temperature ordered-ordered interfaces nearly always involve a disordered phase intermediate. We present a new spectral method for determining the surface tension between phases.

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