Monte Carlo study of the 3-dimensional abelian Higgs model with radially variable Higgs field

The three-dimensional U(1)-Higgs model with a radially variable Higgs field is studied using a Monte Carlo method. The Higgs fields and the U(1) gauge field variables are considered in the same (fundamental) representation. For various small values of the scalar field self-coupling parameter λ, phase transitions (likely first order) between two completely distinct phases of the theory, are observed.     

SU (2) lattice gauge theory and Monte Carlo calculations

Monte Carlo results for theSU (2) lattice gauge theory in four dimensions are presented. The string tension is measured with high statistics and also the mass of the perimeter term is determined. Wilson loop-plaquette correlations, which are related to roughening, are measured.     

Monte Carlo computations in lattice gauge theories

The formulation of gauge theories on Euclidean space-time lattices and the application of the Monte Carlo computational technique to the ensuing systems are reviewed. A variety of numerical results obtained for lattice gauge theories are presented and discussed.     

Monte Carlo integration for lattice gauge theories with fermions

A Monte Carlo procedure is constructed for lattice gauge theories with fermions by replacing integration over fermion degrees of freedom in the path integral by conventional integration over effective boson degrees of freedom. The method is applied to gauge theories over two discrete subgroups of SU(2).     

Monte Carlo simulation of SU(2) gauge theory with fermions on a four-dimensional lattice

After integration over the fermions in an SU(2) lattice gauge theory, the effective fermionic action may be expressed as a sum over all possible closed gauge field loops with corresponding weight factors. We approximate this sum and perform a Monte Carlo simulation of a coupled fermion-gauge system on a 4⁴ lattice. We compare our results for 〈S_eff〉 and $\text{〈}\text{ψ}\text{ψ〉}$ for different values of the gauge field coupling β and fermion coupling κ with the free fermion theory on a lattice. 〈S_eff〉 turns out to be quite small for $\text{κ?}\text{1}\text{8}$.     

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..     

Phase structure of a Z2 lattice gauge theory coupled to a radially variable scalar field

Using Monte Carlo techniques and mean field method, we study a coupled Z₂ gauge-scalar system on a lattice without freezing the radial mode of the scalar field. We find that the phase diagram for our model makes a decided contrast with that for the coupled gauge-spin model when the self-coupling of the scalar field is small. First-order phase transitions caused by the radial fluctuation of the scalar field are observed.     

Glueball masses and symmetry restoration inSU(3) lattice gauge theory: A high statistics Monte Carlo study

We calculate 0⁺⁺, 2⁺⁺ and 1^?+ correlation functions for a wide range of momenta in a high statisticsSU(3) study on an 8⁴ lattice: 28,000 sweeps at β=5.7 and 18,000 at β=5.9. We obtain an accurate confirmation of the restoration of the continuum relativistic dispersion relation,E ²=p ²+m ², and of rotational invariance. We obtain accurate 2⁺⁺ mass estimates up to two lattice spacings, and confirm consistency with asymptotic scaling. For the 1^?+ the results are much poorer and we can only present some very crude mass estimates. We compare our 0⁺⁺ data to our previous calculations with a source, and make some statements about the relative efficiencies of source and variational calculations in this range of couplings.     

Monte Carlo study of the Ising antiferromagnetic with a longitudinal field on the anisotropic square lattice

The Ising antiferromagnetic in the presence of a magnetic field on an anisotropic square lattice is studied by Monte Carlo simulation. We obtained the phase diagram in the T-H plane investigating the reentrant behavior around of the critical field Hc=2Jy. Using the Binder cumulant we locate the critical temperature Tc as a function of H. In order to test our simulation, for null field we obtain the critical behavior of Tc as a function of r=Jy/Jx and is in excellent agreement with exact solution of Onsager. Our results indicate a second-order transition for all values of H and particular case r=1 (independent of the ratio r≠0), where not reentrant behavior was observed.     

A comparison between Monte Carlo algorithms for simulating lattice gauge theories

We compare three updating methods (Metropolis, heat bath and overrelaxed) for pure lattice quantum chromodynamics, by directly measuring their efficiency in a typical mass calculation.     

Monte Carlo variational study of glueball masses in SU (2) lattice gauge theory for coupling less than one

A Monte Carlo variational calculation of glueball masses is performed in SU (2) lattice gauge theory for coupling less than 1. The preliminary upper bounds are obtained, on a 4³×8 lattice, M(0⁺)=1.38±0.26 GeV, M(2⁺)=1.39±0.41 GeV. Evidence of the existence of differences from the results for g²> 1 is observed.     

The mean field perturbation theory of lattice gauge models with covariant gauge fixing

A mean field perturbative expansion with covariant gauge fixing is derived. It is proved that it reproduces the perturbative series at β→∞ in the case of the free energy density to the ordersO(β),O(lnβ),O(l) at least.     

Monte Carlo study of noncompact lattice QCD

We study a noncompact version of lattice QCD₄ by Monte Carlo simulation. The results indicate that the model possesses asymptotic freedom but does not confine static quarks. It looks rather like a self-Higgsed system.     

Monte Carlo study of an Ising gauge system

The phase diagram of the 3-d Ising gauge model with additional ferromagnetic nearest neighbour Ising coupling is explored by Monte Carlo simulations.     

Phase structure of the SU(2) lattice gauge Higgs theory

Phase structure of the SU(2) lattice gauge Higgs theory is investigated by the Monte Carlo method and by an approximate calculation of an effective potential. Higgs fields are considered in the fundamental representation, and the radial mode of Higgs fields is not frozen. Two different radial measures for a radially varied Higgs field are used.Phase diagrams of the theory are determined, and a strong dependence on the choice of radial measure of scalar fields is manifested.