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Register a new userFinite size effects at phase transition in compact U(1) gauge theory
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Authors
Claude Roiesnel
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We present and discuss the results of a Monte-Carlo simulation of the phase transition in pure compact U(1) lattice gauge theory with Wilson action on a hypercubic lattice with periodic boundary conditions. The statistics are large enough to make a thorough analysis of the size dependence of the gap. In particular we find a non-zero latent heat in the infinite volume limit. We also find that the critical exponents $ u$ and $alpha$ are consistent with the hyperscaling relation but confirm that the critical behavior is different from a conventional first-order transition.
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We study the three-dimensional U(1)+Higgs theory (Ginzburg-Landau model) as an effective theory for finite temperature phase transitions from the 1 K scale of superconductivity to the relativistic scales of scalar electrodynamics. The relations between the parameters of the physical theory and the parameters of the 3d effective theory are given. The 3d theory as such is studied with lattice Monte Carlo techniques. The phase diagram, the characteristics of the transition in the first order regime, and scalar and vector correlation lengths are determined. We find that even rather deep in the first order regime, the transition is weaker than indicated by 2-loop perturbation theory. Topological effects caused by the compact formulation are studied, and it is demonstrated that they vanish in the continuum limit. In particular, the photon mass (inverse correlation length) is observed to be zero within statistical errors in the symmetric phase, thus constituting an effective order parameter.
We investigate the continuum limit of a compact formulation of the lattice U(1) gauge theory in 4 dimensions using a nonperturbative gauge-fixed regularization. We find clear evidence of a continuous phase transition in the pure gauge theory for all values of the gauge coupling (with gauge symmetry restored). When probed with quenched staggered fermions with U(1) charge, the theory clearly has a chiral transition for large gauge couplings. We identify the only possible region in the parameter space where a continuum limit with nonperturbative physics may appear.
We investigate four-dimensional compact U(1) lattice gauge theory with a monopole term added to the Wilson action. First we consider the phase structure at negative $beta$, revealing some properties of a third phase region there, in particular the existence of a number of different states. Then our present studies concentrate on larger values of the monopole coupling $lambda$ where the confinement-Coulomb phase transition turns out to become of second order. Performing a finite-size analysis we find that the critical exponent $ u$ is close to, however, different from the gaussian value and that in the range considered $ u$ increases somewhat with $lambda$.
We calculate the energy gap (latent heat) and pressure gap between the hot and cold phases of the SU(3) gauge theory at the first order deconfining phase transition point. We perform simulations around the phase transition point with the lattice size in the temporal direction $N_t=6,$ 8 and 12 and extrapolate the results to the continuum limit. The energy density and pressure are evaluated by the derivative method with nonperturabative anisotropy coefficients. We find that the pressure gap vanishes at all values of $N_t$. The spatial volume dependence in the latent heat is found to be small on large lattices. Performing extrapolation to the continuum limit, we obtain $Delta epsilon/T^4 = 0.75 pm 0.17$ and $Delta (epsilon -3 p)/T^4 = 0.623 pm 0.056.$ We also tested a method using the Yang-Mills gradient flow. The preliminary results are consistent with those by the derivative method within the error.
We study analytically and numerically the three-dimensional U(1) lattice gauge theory at finite temperature in the dual formulation. For an appropriate disorder operator, we obtain the renormalization group equations describing the critical behavior of the model in the vicinity of the deconfinement phase transition. These equations are used to check the validity of the Svetitsky-Yaffe conjecture regarding the critical behavior of the lattice U(1) model. Furthermore, we perform numerical simulations of the model for $N_t = 1, 2, 4, 8$ and compute, by a cluster algorithm, the dual correlation functions and the corresponding second moment correlation length. In this way we locate the position of the critical point and calculate critical indices.
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