Generalized Potts-Models and their Relevance for Gauge Theories

Abstract

We study the Polyakov loop dynamics originating from finite-temperature Yang-Mills theory. The effective actions contain center-symmetric terms involving powers of the Polyakov loop, each with its own coupling. For a subclass with two couplings we perform a detailed analysis of the statistical mechanics involved. To this end we employ a modified mean field approximation and Monte Carlo simulations based on a novel cluster algorithm. We find excellent agreement of both approaches. The phase diagram exhibits both first and second order transitions between symmetric, ferromagnetic and antiferromagnetic phases with phase boundaries merging at three tricritical points. The critical exponents $\nu$ and $\gamma$ at the continuous transition between symmetric and antiferromagnetic phases are the same as for the 3-state spin Potts model.

arXiv commentThis is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 2006, Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

References in corpus (10)

• Three-dimensional antiferromagnetic q-state Potts models: application of the Wang-Landau algorithm
• Critical behaviour of SU(2) lattice gauge theory. A complete analysis with the ${\chi }^2$-method
• Phase Structure of Z(3)-Polyakov-Loop Models
• Effective Actions for the SU(2) Confinement-Deconfinement Phase Transition
• Effective lattice theories for Polyakov loops
• Glauber dynamics of phase transitions: SU(3) lattice gauge theory
• The 3-state Potts model as a heavy quark finite density laboratory
• The Center symmetry and its spontaneous breakdown at high temperatures
• SU(N) Glueball Masses in 2+1 Dimensions
• Critical exponents for higher-representation sources in 3D SU(3) gauge theory from CFT

Cited by in corpus (3)

• Casimir Scaling and String Breaking in G(2) Gluodynamics
• Phase diagram of the lattice G(2) Higgs Model
• More on Algebraic Structure of the Complete Partition Function for the $Z_n$ - Potts Model, Part 1