Phase diagram of the lattice G(2) Higgs Model

TL;DR

This paper maps the phase diagram of the G(2) Higgs model at finite temperature, revealing first and second order transitions, a crossover region, and monopole-driven bulk transitions, using an efficient Monte Carlo algorithm.

Contribution

It provides the first detailed phase diagram of the G(2) Higgs model, identifying the nature and connections of various phase transition lines.

Findings

First order confinement-deconfinement transitions at the limits of the model.

Existence of a small gap where transitions change from first order to continuous.

Presence of a monopole-driven bulk transition line unaffected by confinement transitions.

Abstract

We study the phases and phase transition lines of the finite temperature G(2) Higgs model. Our work is based on an efficient local hybrid Monte-Carlo algorithm which allows for accurate measurements of expectation values, histograms and susceptibilities. On smaller lattices we calculate the phase diagram in terms of the inverse gauge coupling $\beta$ and the hopping parameter $\kappa$. For $\kappa\to 0$ the model reduces to G(2) gluodynamics and for $\kappa\to\infty$ to SU(3) gluodynamics. In both limits the system shows a first order confinement-deconfinement transition. We show that the first order transitions at asymptotic values of the hopping parameter are almost joined by a line of first order transitions. A careful analysis reveals that there exists a small gap in the line where the first order transitions turn into continuous transitions or a cross-over region. For $\beta\to\infty$ the gauge degrees of freedom are frozen and one finds a nonlinear O(7) sigma model which exhibits a second order transition from a massive O(7)-symmetric to a massless O(6)-symmetric phase. The corresponding second order line for large $\beta$ remains second order for intermediate $\beta$ until it comes close to the gap between the two first order lines. Besides this second order line and the first order confinement-deconfinement transitions we find a line of monopole-driven bulk transitions which do not interfer with the confinement-deconfinment transitions.