Phase structure ofZ(3)-Polyakov-loop models

Abstract

We study effective lattice actions describing the Polyakov loop dynamics originating from finite-temperature Yang-Mills theory. Starting with a strong-coupling expansion the effective action is obtained as a series of Z(3)-invariant operators involving higher and higher powers of the Polyakov loop, each with its own coupling. Truncating to 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 concerning the phase structure of the theories. 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 ν and γ at the continuous transition between symmetric and anti-ferromagnetic phases are the same as for the 3-state Potts model.

New phases ofSU(3)andSU(4)at finite temperature

“…However, phases can often be reached in different ways in the space of parameters. The skewed phase we have found in SU(3) gauge theory is very similar to the anti-center phase found in SU(3) spin systems by Wozar et al [14]. Although the term in the spin Hamiltonian that produces the anti-center phase is associated with the 15 representation rather than the adjoint term we have used, we are confident that the two phases will prove to be related.…”

Phase diagram of the latticeG2Higgs model

“…Below the critical temperature is P( x) uniformly distributed over the group manifold and above the critical temperature it is in the neighborhood of a center-element. Near the transition point its dynamics is successfully described by effective three dimensional scalar field models for the characters of P( x) [1][2][3]. If one further projects the Polyakov loops onto the center of the gauge group, then one arrives at generalized Potts models describing the effective Polyakov-loop dynamics [4].…”

No coincidence of center percolation and deconfinement in SU(4) lattice gauge theory

“…Indeed, any such model contains Polyakop loops in the three fundamental representations, the 4,4, and the 6. Depending on the relative weight, the effective theory can be any type of model from a 4-state Potts model to two non-interacting Ising models [13,14]. This would correspond to regarding the center either as Z 4 or as Z 2 × Z 2 .…”