Phase diagram of the latticeG2Higgs model

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 $\ensuremath{\beta}$ and the hopping parameter $\ensuremath{\kappa}$. For $\ensuremath{\kappa}\ensuremath{\rightarrow}0$ the model reduces to ${G}_{2}$ gluodynamics and for $\ensuremath{\kappa}\ensuremath{\rightarrow}\ensuremath{\infty}$ 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 crossover region. For $\ensuremath{\beta}\ensuremath{\rightarrow}\ensuremath{\infty}$ 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 $\ensuremath{\beta}$ remains second order for intermediate $\ensuremath{\beta}$ 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 interfere with the confinement-deconfinment transitions.