K.J.M. Moriarty

Monte-Carlo simulation of pure U(N) and SU(N) lattice gauge theories with fundamental and adjoint couplings☆

Title ofprogram: SUUNFA theories,QED andQCDmodels,non-perturbative ffects,phase transitions, confining and deconfining phases,quark theory, Cataloguenumber:AAOT statisticalmechanicalanalogies, actionper plaquette,Metropolis algorithm, MonteCarlo techniques Programavailablefrom: CPC ProgramLibrary, Queen’sUniversityof Belfast,N. Ireland(seeapplicationformin this issue) Natureof thephysicalproblem The program simulates thermal equilibrium for U(N) and Computer: CDC 6600, CDC 7600; Installation: University of SU(N) latticegaugetheorieswith couplingsin both thefundaLondonComputerCentre mentalandadjointrepresentations. Gaugetheorieson a lattice were originally proposedby Wilson [1] andPolyakov121. Operatingsystem:CDC NOS/BE,SCOPE Methodofsolution Programminglanguage: FORTRAN IV with a few CDC nonA MonteCarlo simulationof the systemset up on a latticeof standardfeatures variabledimensionalityandlatticesizegeneratesa sequenceof field configurationson the lattice links. TheMetropolis algoHigh speedstoragerequired: 26 K (maximum) rithm [3], originally developedfor Monte Carlo simulationsin statisticalmechanics, is usedto generatestatisticalequilibrium. Numberof bits in a word: 60 Newconfigurationsaregeneratedlink by link andconvergence to equilibrium is acceleratedby performing the Metropolis Peripheralsused: card reader,line printer algorithmNTMAX timeson a givenlink beforepassingto the next link. The matrix for a given link is updatedusinga table Numberof cardsin combinedprogram and testdeck: 852 of matricesof the correct group symmetry. The programpermits thechoiceof a cold (ordered)orhot (disordered)start. Cardpunchingcode: CDC Restrictionon thecomplexityof theprogram

MONTE CARLO STUDIES OF WILSON LOOPS IN FOUR-DIMENSIONAL U(2) GAUGE THEORY

Abstract 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 = βc, where βc 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 studies of SU(N)/ZN lattice gauge theories in four dimensions

Abstract Using Monte Carlo techniques on a four-dimensional space-time lattice, we study SU(N)/ZN gauge theories for N = 3, 4, 5 and 6. We find first-order phase transitions at critical inverse temperatures of βc = 6.40, 12.0, 19.5 and 32.0 and SU(3)/Z3,SU(4)/Z4,SU(5)/Z5and SU (6)Z6, respectively.

Quantum chromodynamics on a simplical lattice

Abstract Monte Carlo simulations on a 64 simplicial lattice are used to calculate Wilson loops, and hence the string tension, for pure SU(3) gauge theory. The asymptotic freedom scale parameter Λ is measured for both triangles and squares and universality is established.

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

Abstract Monte Carlo results for the pure U(3) lattice gauge theory on a 6 4 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..

An application of the Ringland-Roberts-Roytran Thanh Van Reggeized absorption model to hypercharge-exchange reactions

The 0−1/2+ → 0−1/2+ hypercharge-exchange reactions: π+p → K+Σ+, K−p → π−Σ+, K−p → πoΛ, K−p → ηΛ, K−p → η′Λ, π−p → KoΛ, π−p → KoΣo, K−n → π−Λ and K−n → π−Σo are studied within the framework of a Reggeized absorption model recently proposed by Ringland, Roberts, Roy and Tran Thanh Van. The use of SU (3) symmetry and strong exchange degeneracy gives all the parameters for the pole graphs with the exception of the spin non-flip and spin flip D/F ratios. The absorptive corrections are applied in the normal manner to the rotating phase part of the pole-graph amplitude but an additional phase of 1/2π is included in the absorptive correction for the non-rotating phase part of the pole-graph amplitude. The agreement between the theoretical predictions and the experimental data on differential cross sections and polarizations is extremely good.

The phase diagrams for SU(N)-SU(N)/ZN, N=3-8, gauge theories in four dimensions

By computer simulation, we study SU(N) lattice gauge theory with an action containing couplings with the plaquette trace in both the fundamental and adjoint representations of the group. We investigate whether such an action will permit continuation around the phase transition of the Wilson theory when N exceeds four. By extrapolating this transition to where its latent heat vanishes, we locate the corresponding critical points for N up to eight. The phase structure of lattice gauge theory has been of crucial importance to our understanding of quark confinement. The absence of phase transitions in the four- dimensional models based on SU(2) (Creutz 1979) and SU(3) (Creutz and Moriarty 1982b, Ardill et a1 1983a) indicates that the linear interquark potential at large separations persists from the strong-coupling into the weak-coupling domain. Recently, this simple picture acquired a fascinating complication with the discovery of phase transitions in the Wilson theory when the gauge group is SU(N) with N>4 (Creutz 1981, Moriarty 1981, Bohr and Moriarty 1981, Creutz and Moriarty 1982a). It was suggested by Creutz (1981) that these transitions were not deconfining, but could be continued around in a larger coupling space. It was later found that SU(2) (Halliday and Schwimmer 1981a, b, Greensite and Lautrup 1981, Bhanot and Creutz 1981) and SU(3) (Bhanot 1982) theories possessed a rich phase structure with such an extension. In this paper, we investigate larger4 models with both fundamental and adjoint couplings and find evidence that the transition with the Wilson action is indeed spurious and is easily continued around. We work on a hypercubical lattice in four Euclidean space-time dimensions. Our

Wilson loops in quenched, reduced N=∞QCD

The authors study Wilson loops up to size 3*3 in the quenched, reduced large-N lattice gauge theory for N=40. Because of finite-size effects, scaling of asymptotic freedom is not observed.