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.     

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.     

Monte Carlo studies of wilson loops in four-dimensional U(2) gauge theory

Wilson loops are calculated using Monte Carlo simulations for pure U(2) gauge theory on a 6⁴ lattice. The loops appear to contain an area law piece in both the high and low temperature regions. The string tension is discontinuous at β = β_c, where β_c is the critical inverse temperature. This suggests that the first-order phase transition in U(2) gauge theory is not a deconfining phase transition. The determinant of the Wilson loop, however, extracts the U(1) part of the theory and appears to lose the area law at low temperature.     

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 $\text{κ?}\text{1}\text{8}$.     

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.     

Excited glueball states in four-dimensional SU(3) lattice gauge theory

For SU(N) (N ? 2) lattice gauge theories in four dimensions we construct all irreducible representations of the full cubic group on spacelike Wilson loop operators up to length 6. Relying on this set of operators preliminary Monte Carlo results for SU(3) excited glueball states are reported.     

Monte Carlo study of U(1) and SU(2) gauge fields on four-dimensional random lattices

The asymptotic behavior of the random lattice gauge model is examined. Numerical results of the specific heat of U(1) and SU(2) on the random lattices of a different number of sites in four dimensions are reported and the phase structure is discussed.     

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 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.     

Some calculations in lattice gauge theory

We look at the action proposed by Wilson on a lattice and calculate static constants like f_π and two-body decay amplitudes in a certain approximation. Results are good to factors of four to six. There is good agreement for some of the predicted meson masses.     

Monte Carlo calculations on the gauge Potts model

Theq-state gauge Potts modelP _q ind-dimensions has been studied using Monte Carlo techniques. Ford=2 no phase transitions were detected. TheP ₂ model ford=3 shows a second order phase transition. On the other hand, all thed=3 (q2) andd=4 cases studied show first order phase transitions. In these cases, it was possible to estimate transition coupling parameters as well as latent heat. For selected cases, a study of the behavior of the Wilson loop factor was done.Partially supported by CONICET, CIC Pcia. de Buenos Aires and SUBCYT, Argentina     

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.     

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).     

How well do Monte Carlo simulations distinguish between U(1) and SU(2)?: A study of the string tension in U(1) lattice gauge theory

To investigate how a system with a known deconfining phase transition behaves when studied on finite lattices via Monte Carlo simulations, we have made such studies of compact U(1) lattice gauge theory for 8⁴, 10⁴, and 12⁴ lattices. We have concentrated on the mean plaquette energy and the string tension. The string tension does not vanish on a finite lattice, but using finite size scaling arguments the indications are that it does vanish on an infinite lattice, where we predict the critical coupling β_c = 1.008 and the correlation length exponent $\text{ν =}\text{1}\text{3}$. We compare our results to those for SU(2) and find that although there are differences, they are not yet definitive.     

Thermodynamics of SU(3) lattice gauge theory

The pressure and the energy density of the SU(3) gauge theory are calculated on lattices with temporal extent N_τ = 4, 6 and 8 and spatial extent N_σ = 16 and 32. The results are then extrapolated to the continuum limit. In the investigated temperature range up to five times T_c we observe a 15% deviation from the ideal gas limit. We also present new results for the critical temperature on lattices with temporal extent N_τ = 8 and 12. At the corresponding critical couplings the string tension is calculated on 32⁴ lattices to fix the temperature scale. An extrapolation to the continuum limit yields T_c/√σ = 0.629(3). We furthermore present results on the electric and magnetic condensates as well as the temperature dependence of the spatial string tension. These observables suggest that the temperature dependent running coupling remains large even at T ≅ 5T_c. For the spatial string tension we find √σ_s/T=0.566(13)g²2(T) with g² (5T_c) ≅ 1.5.