Variational Calculation of Lattice SU(N)/ZN Gauge Systems for N = 3~6

A variational calculation scheme of SU(N)/Z_N lattice gauge models for large but finite N is presented. The order parameter, the internal energy (E), and the phase transition points of lattice SU(N)/Z_N gauge systems for N = 3~6 are calculated. The results of (E) are in good agreement with Monte Carlo simulations.     

Variational method in hamiltonian lattice gauge theories

A general expression for the expectation value of the hamiltonian of a d + 1 dimensional lattice gauge theory as a function of the norm of the variational state (that itself has the form of a partition function of a d-dimensional lattice gauge theory) is given. Applications include U(1), SU(2), U(2) and U(N) gauge theories for large N in d = 2 + 1 dimensions. It is also demonstrated that the deconfining phase transition is of first order in every dimension above the critical one, provided it is of first or second order at the critical dimension.     

Investigation of U(1) Lattice Gauge Model at Finite Temperature to Higher Order Expansion

The cumulant expansion of U(1) lattice gauge model at finite temperature (N_T=1) to the sixth order is presented. The variational parameters are determined by requiring thatthe corrections to the zeroth order approximation are the smallest. The order parameter,Polyakov line , converges well and is in good agreement with Monte Carlo simulations.Especially, the deconfinement phase transition point can be determined with accuracy.     

Phase structure of QCD at high temperature with massive quarks and finite quark density: A Z(3) paradigm

The confinement/deconfinement phase transition in SU(3) lattice gauge theories at high temperatures is analogous to that of the Z(3) gauge theories. We study various Z(3) gauge-matter theories that result from replacing the gauge group SU(3) with its center Z(3). We include large-mass fermions in the Wilson formulation and allow a chemical potential. We show that in the limit of strong coupling and high temperature the (3 + 1)-dimensional theory becomes a three state, three-dimensional Potts model with uniform external fields of real and imaginary strengths related to the fermion mass and chemical potential. By studying the phase structure of the q = 3, d = 3 Potts model with external fields we argue that the confinement/deconfinement phase transition is first order, but highly sensitive to external fields, and that it does not occur at “strong coupling” in a Z(3) gauge theory if there is a light enough fermion present. We discuss the consequences of this result for QCD.     

Finite Temperature Phase Structure for SU(2) with a Mixed Action

The modified Migdal-Kadanoff (MK) renormalization transformation is applied to SU(2) lattice gauge theory (LGT) with a mixed action at finite temperature. The renormalization trajectory distributions and the phase structures in the whole coupling parameter space are obtained. Using the dependence of transition temperature on the coupling, the scaling behavior is found in the weak coupling region of β≥1.20. Numerical calculation gives the value of critical temperature T_c = 0.682A_mom. It is close to the data from the Monte Carlo simulation.     

SU(2)格点规范理论SIN作用量在有限温度下的解除禁闭的相变

我们对SU(2)群格点规范理论的Sinl-Sin((1/2)T_rU_p)作用量做了有限温度下的Monte Carlo计算,观察到一个高温下解除禁闭的相变。临界点是Tc≈334±40Mev,这与使用Wilson作用量及其它类型作用量所得结果可以相容。     

ANALYTIC STUDY OF su(3) LATTICE GAUGE THEORY

The variational-cumulant expansion method has been extended to the case of lattice SU(3) Wilson model.The plaquette energy as an order parameter has calculated to the 2nd order expansion.No 1st order phase transition in the d=4 case is found which is in agreement with the monte Carlo results,and the 1st order phase transition in the d=5 case is clearly seen.The method can be used in the study of problems is LGT with SU(3) gauge group.     

Calculation of Vacuum Wavefunction and Mass .Gap from Improved (2+l)-Dimensional SU(2) Lattice Gauge Field Hamiltonian

The truncated eigenvalue equation of SU(N) lattice gauge theory is studied by using improved lattice gauge Hamiltonian with a proper truncation scheme that preserves the continuum limit. The calculations of vacuum state wavefunction and glueball mass of (2+1)-dimensional SU(2) theory up to third order are carried out, the results show the improvement of scaling behavior in deep weak coupling region.     

VARIATIONAL TREATMENT WITH THE THIRD ORDER CORRECTIONS FOR SU(2) LATTICE GAUGE THEORY

The variational method in Lagrangian formalism in lattice gauge theory in cumulant expansion is discussed. For SU(2) pure gauge Wi1son model to the third order corrections we show that there is no phase transition in four dimensions, but there exists the first order phase transition in five dimensions at β_C=0.838 in agreement with the Monte Carlo results. The physical meaning of higher order corrections is discussed.     

THE EVIDENCE OF DECONFINEMENT PHASE TRANSITION OF SU(2) LATTICE GAUGE MODEL BY MONTE CARLO METHOD

In this paper,we have calculated the SU(2) lattice gauge by the Monte Carlo method.For the finite temperature problem 8³×4 lattice is used and for the zero temperature problem 8⁴ lattice.From the calculations of the energy density,heat capacity and entropy density,the results indicate that there is a deconfinement phase transition when T/Λ_L=40—50.     

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.     

Analytic approximations to hamiltonian lattice field theories: (I). Periodic gaussian model for U(1) theories

Periodic gaussian models are introduced for local and global U(1) invariant hamiltonian lattice field theories. The models coincide with standard lattice theories at weak coupling, but the leading non-perturbative contributions to wave functions and physical quantities are exactly calculable. Electric charges are confined and the mass gap is finite if correlations of an integer-valued magnetic field are of infinite range (d = 2 + 1 gauge model). Otherwise, for short-range correlations, the mass gap and the string tension vanish at weak coupling (QED, XY model, etc.)     

Analytic calculation of Glueball Mass In (2+1)-D SU(2)Lattice Gauge Theory

In this paper,the glueball mass of 0⁺⁺ is calculated in the (2+1)－D SU(2) lattice gauge theory with connection graphs.The result shows a good scaling behavior.     

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.     

A study of the bulk phase transitions of the SU(2) lattice gauge theory with mixed action

Using the finite size scaling theory, we reexamine the nature of the bulk phase transition in the fundamental-adjoint coupling plane of the SU(2) lattice gauge theory at β_A = 1.25 where previous finite size scaling investigations of the deconfinement phase transition showed it to be of first order for temporal lattices with four sites. Our simulations on N⁴ lattices with N = 6, 8, 10, 12 and 16 show an absence of a first order bulk phase transition. We find the discontinuity in the average plaquette to decrease approximately linearly with N. Correspondingly, the plaquette susceptibility grows a lot slower with the 4-volume of the lattice than expected from a first order bulk phase transition.     

Thied—Order Approximation of 0^＋＋ Glueball Mass and Wavefunction of （2＋1）—Dimensional SU（3） Lattice Gauge Theory

The random phase approximation is applied to the coupled-cluster expansions of lattice gauge theory (LGT) Using this method,wavefuctions are approximated by linear combination of graplh consisting of only one connected wilson loop.We study the excited state energy and wavelunction in (2 1)-D SU(3) LGT up to the thired order,The glueball mass shows a good scaling behavior.     

Linked cluster expansions for U(1) lattice gauge theory in 2 + 1 and 3 + 1 dimensions

Compact U(1) lattice gauge theory is studied in 2 + 1 and 3 + 1 dimensions using strong coupling series expansions and the recently proposed exact linled cluster expansion alborithm Results for the vacuum energy, specific heat and axial string tension in 2 + 1 dimensions are in agreement with previous finite lattice estimates. In 3 + 1 dimensions, we present new strong coupling series results (order g^?40) which together with the ELCE estimates show evidence of a continuous phase transition at x = 1/g⁴ = 0.72 ± 0.08. The associated critical index for the vanishing string tension is μ = 0.65 ± 0.12. The axial string tension in D = 3 + 1 appears to undergo a non-deconfining roughening transition at smaller x (0.56 ± 0.07).     

Variational Cumulant Expansion on SU(2)⊗ SU(2) Chiral Model

The phase transition of the two-dimensional SU(2)⊗ SU(2) lattice chiral model has been studied by a variational cumulant expansion method. The internal energy and the specific heat are calculated to the 4th order correction and they are in good agreement with the Monte Carlo (MC) resdits. Except the behavior of the crossover region, similarities between this model and the four-dimensional SU(2) lattice gauge model are also discussed.     

Wilson loops for U(4) and SU(4) lattice gauge theories in four dimensions

Monte Carlo simulations are used to calculate Wilson loops for pure U(4) and SU(4) gauge theories on a 6⁴ lattice. The first-order phase transitions previously observed in the average action per plaquette for U(4) and SU(4) is also seen in the string tension. U(4) and SU(4) color seem to be confined while U(4) charge in U(4) appears to be deconfined.     

The Deconfinement Transition in SU(2) Lattice Gauge Theory:An Analytical Study

We study SU(2) lattice gauge theory at finite temperature in the variational cumulant expansion approach. The deconfinement transition is given in four and five dimensions. The comparison with Monte Carlo results ia also presented.