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.     

The string tension and the scaling behavior of SU(2) gauge theory on a random lattice

The SU(2) gauge theory on an 8⁴ random lattice has been studied by the Monte Carlo method. The string tensions have been evaluated. They display the expected scaling behavior for β=1.2−1.3. The scale parameter Λ_RAN has been determined approximately.     

Scaling behaviour of Creutz ratios inSU(2) lattice gauge theory

An analysis of the scaling behaviour of Creutz ratios on large lattices is given forSU(2) gauge theory. The β-interval is 2.5≦β≦2.8. Under a factor 2 scaling test, after multiplicative corrections for lattice artifacts, the Monte Carlo data show deviations from scaling, which are similar for all values of β. The ratios can be fitted successfully by a sum of three perturbative terms and an exponentially decreasing nonperturbative term. For many ratios the latter turns out to be very small, and its size dependence at fixed β is consistent with that of an area term in the Wilson loops. The deviation of the corresponding exponents from the ones expected for an area term gives a coherent cxplanation of the observed departures from scaling. It is well possible that for fixed spatial extension (in lattice units) nonperturbative contributions vanish so fast that they cannot be interpreted as physical effects.     

String tension in SU(3) lattice gauge theory

Wilson loop expectation values have been determined in SU(3) lattice gauge theory without fermions using Monte Carlo methods and considering lattices of up to 10⁴ sites. A heat bath technique has been developed in order to enhance the statistical independence of successive lattice configurations.     

Scaling behaviour of small volume physics inSU(2) lattice gauge theory

A factor 2 scaling test for masses, derived from the correlation function of Polyakov loops, has been performed on physically small lattices with high precision. The test has been made at β=2.9 and β=3.0, comparing masses on lattices of size 16³·128 and 16³·192 resp. with masses on half sized lattices. Results for Δβ are significantly higher than those obtained by MCRG methods, by Creutz ratios and by the string tension on larger lattices. They are almost compatible with asymptotic scaling.     

Scaling in lattice QCD: Glueball masses and string tension

We study the scaling behaviour of lattice quantum chromodynamics by comparing the β dependence of the string tension and the 0⁺⁺ glueball mass. We use a source method at β=5.7, β=5.9 and β=6.1, on lattices from 9³· 24 to 16³· 32. Assuming a string tension of about (420 MeV)², the lattice spacing ranges from 0.16 to 0.08 fm. In order to separate finite volume from scaling violation effects we have compared data from lattices having approximately the same overall physical size at the different values of β. We find deviations from scaling to be very small.     

Universality in SU(2) lattice gauge theory

A method of resumming perturbation theory is used to re-analyze previous Monte Carlo data of Bhanot and Dashen. We find no inconsistency with universality. There appears to be a relatively large region where Monte Carlo studies can reliably be done.     

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.     

Finite temperature SU(2) lattice gauge theory

We discuss SU(2) lattice gauge theories at non-zero temperature and prove several rigorous results including i) the absence of confinement for sufficiently high temperature in the pure gauge theory, and ii) the absence of spontaneous chiral symmetry breaking for sufficiently high temperature in the theory with massless fundamental representation fermions.     

Finite tension strings in SU(2) gauge theory

The second-order field equations of the SU(2) Higgs model are studied and a new class of string solutions is obtained. The tension is finite and scale-dependent and the strings are of minus one unit flux.     

Confining string formed by P vortices in the indirect Z(2) projection of SU(2) lattice gauge theory

We study the distribution of P vortices near the confining string in the indirect _Z(2) projection of SU(2) lattice gauge theory. We find that the density of vortices approaches the vacuum value at large distances and is strongly suppressed near the line connecting the test quark-antiquark pair. This implies that the condensate of P vortices is broken inside the confining string. The width of the _P-vortex density distribution increases with increasing distance between the quark and antiquark. Our best fit indicates the logarithmic dependence of this width on q q? separation.