The Fredenhagen-Marcu operator in the gauge-Higgs Z(2) LGT at finite temperature

TL;DR

Problem addressed: identify a finite-temperature order parameter distinguishing deconfinement from confinement and Higgs phases in gauge theories with dynamical matter. Method: compute the Fredenhagen-Marcu operator in the (2+1)-dimensional $Z(2)$ gauge–Higgs lattice theory via Monte Carlo simulations on large lattices, evaluating $\\rho = \\lim_{R \\to \\infty} H(R,T)$ with $H(R,T)= \\frac{\\langle V(\\mathcal{L}_{xy}) \\rangle^2}{\\langle W(\\mathcal{C}) \\rangle}$. Key results: in the deconfined phase the large-$R$ limit of $\\rho$ vanishes, while in confinement and Higgs phases it tends to a nonzero constant; near the phase transition the constant may shrink with volume and the 2d Ising universality governs the deconfinement transition. Significance: the FM operator provides a nonlocal finite-temperature diagnostic of deconfinement in gauge–Higgs systems, motivating extensions to fermionic matter and potential relevance to QCD-like theories.

Abstract

We explore the possibility to use the Fredenhagen-Marcu operator as an order parameter of the deconfinement phase transition in gauge-matter systems at finite temperature. Concretely, we compute by numerical simulations this operator in the (2+1)-dimensional Z(2) lattice gauge theory (LGT) with Z(2) gauge fields coupled to Z(2)-valued Higgs fields. Our conclusion is that the Fredenhagen-Marcu operator can indeed serve as an order parameter capable of distinguishing the deconfinement phase from the Higgs and confinement phases of the theory.

Figures (8)

• Figure 1: The Polyakov loop susceptibility as a function of $\beta$ at fixed values of $\gamma$ in the region of the second order phase transition for several spatial sizes.
• Figure 2: Collapse of the Polyakov loop susceptibility. Critical indices are fixed to the values in $2d$ Ising model: $\eta=0.25$ and $\nu=1$. "Raw" data refers to the points obtained directly from Monte-Carlo simulations, while "reweighted" data are obtained using the multihistogram reweighting of raw data to intermediate values of gauge coupling $\beta$.
• Figure 3: Collapse of the Polyakov loop susceptibility. Critical indices are fixed to the values in $3d$ Ising model: $\eta\approx0.03629$ and $\nu\approx0.63$. The meanings of the labels are the same as in Fig.\ref{['fig:chi_collapse']}.
• Figure 4: Left: Histogram of the Polyakov loop in the region of the first order phase transition. Right: The Polyakov loop susceptibility in the crossover region.
• Figure 5: Phase diagram of the $Z(2)$ gauge-Higgs theory on the lattice at finite temperature for $N_t=16$. The acronym CEP stands for "critical end point" and MCP for "multicritical point". For other details see text.