Effective Polyakov loop dynamics for finite temperatureG2gluodynamics

Abstract

Based on the strong coupling expansion we obtain effective 3-dimensional models for the Polyakov loop in finite-temperature G2 gluodynamics. The Svetitsky-Jaffe conjecture relates the resulting continuous spin models with G2 gluodynamics near phase transition points. In the present work we analyse the effective theory in leading order with the help of a generalised mean field approximation and with detailed Monte-Carlo simulations. In addition we derive a Potts-type discrete spin model by restricting the characters of the Polyakov loops to the three extremal points of the fundamental domain of G2. Both the continuous and discrete effective models show a rich phase structure with a ferromagnetic, symmetric and several anti-ferromagnetic phases. The phase diagram contains first and second order transition lines and tricritical points. The modified mean field predictions compare very well with the results of our simulations.

Hagedorn spectrum and thermodynamics of SU(2) and SU(3) Yang-Mills theories

“…Besides quantities of most direct phenomenological interest, the constant progress in algorithmic sophistication and in computational power makes it possible to address more fundamental issues, and to generalize the lattice studies of the QGP to QCD-like theories which, although not realized in nature, can provide helpful insight into the structure of non-Abelian gauge theories and can be compared, for instance, to analytical computations based on semiclassical approaches [43]. Examples include finite-temperature lattice studies in pure-glue SU(3) Yang-Mills theory [44][45][46][47][48][49][50], in its generalizations with a larger number of color charges N [51][52][53][54][55][56][57][58][59][60][61][62] and/or to three, rather than four, spacetime dimensions [63][64][65][66][67][68][69][70], or theories based on a center-less exceptional gauge group [71][72][73][74][75].…”

Exceptional thermodynamics: the equation of state of G2 gauge theory

“…In this work, we extend previous lattice studies of G 2 Yang-Mills theory at finite temperature [82][83][84][85] by computing the equation of state in the temperature range T 3T c , where T c denotes the critical deconfinement temperature. 3 After introducing some basic definitions and the setup of our simulations in section 2, we present our numerical results in section 3; then in section 4 we compare them with the predictions of some analytical calculations, pointing out qualitative and quantitative analogies with SU(N ) gauge theories.…”

“…This leaves only G 2 , F 4 and E 8 as compact simply-connected Lie groups with a trivial center; of these, G 2 , with rank two and dimension 14, is the smallest and hence the most suitable for a lattice Monte Carlo study. In fact, numerical simulations of this Yang-Mills theory have already been going on for some years [74][75][76][77][78][79][80][81][82][83][84][85]. Besides numerical studies, these peculiar features of G 2 Yang-Mills theory have also triggered analytical interest [86][87][88][89][90][91][92][93][94][95][96][97].…”

Phase diagram of the latticeG2Higgs model

“…1 which shows the expectation value of P for G 2 gluodynamics as function of the inverse gauge coupling β = 1/g 2 . In an earlier work we derived a 3 dimensional effective theory for the dynamics of the Polyakov loop for finite temperature G 2 gluodynamics and analyzed the resulting Landau-type theory with the help of elaborate Monte Carlo simulations [14]. Already the leading order effective Polyakov loop model exhibits a rich phase structure with symmetric, ferromagnetic, and anti-ferromagnetic phases.…”