The string tension of compact U(1) four-dimensional lattice gauge theory

Monte Carlo simulations of the string tension are calculated for four-dimensional U(1) gauge theory on a 6⁴ lattice. The string tension follows the result -1n(β/2) in the high temperature region and is zero for β > β_c, where β_c is the critical inverse temperature.     

Lorentz gauge and Gribov ambiguity in the compact lattice U(1) theory

The Gribov ambiguity problem is studied for compact U(1) lattice theory within the Lorentz gauge. In the Coulomb phase, it is shown that apart from double Dirac sheets Gribov copies originate mainly from zero-momentum modes of the gauge fields. The removal of the zero-momentum modes is necessary for reaching the absolute maximum of the Lorentz gauge functional.     

Plaquette expansion study of compact U(1) lattice gauge theory in (2 + 1) dimensions

The plaquette expansion is applied to compact U(1) lattice gauge theory in (2 + 1) dimensions to high order: 1/N ⁸ for the ground state energy density and 1/N ⁷ for the anti-symmetric or photon mass gap, where N is defined as the number of plaquettes. Evidence of scaling in the photon mass gap is observed for low order (≤ 1/N ⁴) for inverse coupling values β = 0. 7 to 1. 25 with scaling behaviour given by the weak-coupling formula: M ²/β = exp(-5. 01β + 5. 82) in good agreement with other studies. Higher order results appear to diverge from the scaling slope past the transition point portenting the prospect that the strong coupling trial state in this region gives vise to an asymtotic series in 1/N for the photon mass gap.     

Phase structure of a U(1) lattice gauge theory with dual gauge fields

We introduce a U(1) lattice gauge theory with dual gauge fields and study its phase structure. This system is partly motivated by unconventional superconductors like extended s-wave and d  -wave superconductors in the strongly-correlated electron systems and also studies of the t–J$t\text{–}J$ model in the slave-particle representation. In this theory, the “Cooper-pair” (or RVB spinon-pair) field is put on links of a cubic lattice due to strong on-site repulsion between original electrons in contrast to the ordinary s  -wave pair field on sites. This pair field behaves as a gauge field dual to the U(1) gauge field coupled with the hopping of electrons or quasi-particles of the t–J$t\text{–}J$ model, holons and spinons. By Monte Carlo simulations we study this lattice gauge model and find a first-order phase transition from the normal state to the Higgs (superconducting) phase. Each gauge field works as a Higgs field for the other gauge field. This mechanism requires no scalar fields in contrast to the ordinary Higgs mechanism. An explicit microscopic model is introduced, the low-energy effective theory of which is viewed as a special case of the present model.     

U(2) four-dimensional simplicial lattice gauge theory

Monte Carlo simulations for pureU (2) gauge theory on a four-dimensional simplicial lattice with six sites in each direction are reported. Wilson loops and the string tensions for squares and triangles are presented. A first-order phase transition, similar to that found for the hypercubical lattice, is observed and found to confineSU (2) colour and deconfineU (1) charge.     

U(1) gauge theory on a torus

U(1) gauge theory with the Villain action on a cubic lattice approximation of three- and four-dimensional torus is considered. As the lattice spacing approaches zero, provided the coupling constant correspondingly approaches zero, the naturally chosen correlation functions converge to the correlation functions of theR-gauge electrodynamics on three- and four-dimensional torus. When the torus radius tends to infinity these correlation functions converge to the correlation functions of theR-gauge Euclidean electrodynamics.Supported by the Russian Foundation of Fundamental Researches under Grant 93-011-147     

Order parameters and boundary effects in U(1) lattice gauge theory

We show that, independently of the boundary conditions, the two phases of the 4-dimensional compact U(1) lattice gauge theory can be characterized by the presence or absence of an “infinite” current network, with an appropriate definition of “infinite” network takes values 0 or 1 in the cold and hot phase, respectively. It thus constitutes a very efficient order parameter, which allows one to determine the transition region at low computational cost. In addition, for open and fixed boundary conditions we address the question of the impact of inhomogeneities and give examples of the reappearance of an energy gap already at moderate lattice sizes.     

Deconfinement phase transition in a 3D nonlocal U(1) lattice gauge theory

We introduce a 3D compact U(1) lattice gauge theory having nonlocal interactions in the temporal direction, and study its phase structure. The model is relevant for the compact QED3 and strongly correlated electron systems like the t-J model of cuprates. For a power-law decaying long-range interaction, which simulates the effect of gapless matter fields, a second-order phase transition takes place separating the confinement and deconfinement phases. For an exponentially decaying interaction simulating matter fields with gaps, the system exhibits no signals of a second-order transition.     

Absence of charged states in the U(1) Higgs lattice gauge theory

We show that a sequence of dipole states of finite energy introduced by Fredenhagen and Marcu is chargeless upon removal of one of the charges to spatial infinity in certain subsets of the phase diagram of the U(1)-Higgs lattice gauge theory. It is also explicitly seen how this phenomenon is related to the existence of exponential clustering (i.e., of a mass gap). Related properties of dipole states are briefly discussed.Supported by the Fundacão de Amparo à Pesquisa do Estado de São Paulo (FAPESP). Address after September 1985: II. Institut für Theoretische Physik der Universität Hamburg, Luruper Chaussee 149, D-2000 Hamburg 50, Federal Republic of GermanySupported by FAPESP. Permanent address: Instituto de Fisica, Universidade de São Paulo, São Paulo, Brazil     

Convergence of U(1)3 lattice gauge theory to its continuum limit

It is shown that in three space-time dimensions the pure U(1) lattice gauge theory with Villain action and fixed coupling constant converges to the free electromagnetic field as the lattice spacing approaches zero. The same holds for the Wilson action on the electric sector.     

The mean-field approximation in the SU(2) pure lattice gauge theory

The phase structure of the SU(2) pure lattice gauge theory with two coupling constants is derived in the mean-field approximation. The obtained phase diagram agrees with Monte Carlo results. The technique used here allows the computation of further corrections.     

Quark trapping for lattice U(1) gauge fields

We show for lattice U(1) gauge fields in d = 3 dimensions, that 〈exp(i∮_CAdx)〉 ? exp (? const.T lnL), where C is a rectangle of dimension T × L, T ? L. This indicates quark trapping, by a potential at least as strong as Coulomb.     

U(3) four-dimensional lattice gauge theory and Monte Carlo calculations

Monte Carlo results for the pure U(3) lattice gauge theory on a 6⁴ lattice are reported. Wilson loops and the string tension are presented. The first-order phase transition in U(3) is reflected quite clearly in a discontinuity in the string tension at β = β_c. The U(1) factor of U(3) is extracted using the determinant of the Wilson loops. As expected, the U(1) component appears to deconfine at the phase transition..     

The deconfining transition for finite-temperature U(1) lattice gauge theory in (2 + 1) dimensions

A detailed examination of the deconfining transition in finite-temperature (2 + 1)-dimensional U(1) lattice gauge theory is presented. The transition appears to be of the Kosterlitz-Thouless type, in agreement with the two-dimensional XY model behaviour expected from universality arguments. However, measurements of the critical exponent η of the Wilson line correlation function do not give the predicted XY value.