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1.
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.  相似文献   

2.
High precision data from a variety of sources forSU(2) andSU(3) Wilson action lattice gauge theory are analyzed with respect to the hypothesis of the possible existence of a zero temperature deconfining phase transition, in analogy with theU(1) theory. The internal energy, specific heat, string tension, and Wilson line, fit well to correlation length scaling laws associated with a finite order transition occurring at the weak coupling end of the crossover region for both theories. TheSU(2) theory is consistent with a correlation length exponent ν=2/3 and critical pointβ c ≈2.47. ForSU(3) the data fit well to ν=1 andβ c ≈6.69. Additional indirect evidence for the existence of such phase transitions is discussed, as is the possible crucial role of light dynamical fermions in the confinement mechanism.  相似文献   

3.
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 βc = 1.008 and the correlation length exponent ν = 13. We compare our results to those for SU(2) and find that although there are differences, they are not yet definitive.  相似文献   

4.
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 > βc, where βc is the critical inverse temperature.  相似文献   

5.
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).  相似文献   

6.
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.  相似文献   

7.
We determine numerically, and display graphically, the electromagnetic energy distribution due to static sources in compact QED3. Using the polymer formulation of the functional integral, Monte Carlo simulations are performed with external sources included in the lattice action. Both the Wilson and Villain forms of the action are studied, and the string tension is determined in a small range of weak couplings. For the Villain action, our values for the string tension σ are in agreement with Polyakov's formula. For the Wilson action, we are able to detect a string tension in a range of weak couplings 2.1 ? β ? 2.3 below the weak-to-strong coupling cross-over point. In the same range, standard Monte Carlo results for up to 8 × 8 Wilson loops are consistent with ordinary perturation theory (no confinement). A possible explanation of this discrepancy is discussed, and it is suggested that the standard (source-free) Monte Carlo might miss configurations which are important for flux-tube formation.  相似文献   

8.
We report the results of hadron mass calculations in the valence (quenched) approximation, on an 83 × 16 lattice. For Wilson fermions with the standard Wilson action we find good agreement with results form the hopping parameter expansion on a 164 lattice at β = 5.7, with only a small finite size effect in the anticipated direction. The proton-to-rho mass ration is however too high by 60% and the delta-proton mass difference is too small. We have repeated these calculations at two points of the same string tension in the plane of the fundamental and adjoint couplings, in an attempt to avoid the unphysical critical point there; within statistical errors the meson masses remain the same, there is an improvement in the delta-proton splitting and the proton mass decreases slightly, but not enough to produce agreement with experiment. The estimates of lines of constant string tension obtained as a preliminary to the mass calculation are in good agreement with weak coupling expansions at the larger β values and cross over towards strong coupling predictions around β = 5.7. Also, crude estimates reveal the disappearance of the specific heat peak as one moves away from the unphysical singularity. For Susskind fermions we find some measure of agreement with other results form a 103 × 16 lattice, but large, apparently finite size, effects in the rho mass at low quark mass. Meson masses in lattice units disagree with the Wilson fermion results by as much as a factor of 2. This disagreement persists in the fundamental-adjoint plane, suggesting the importance of studying improved fermion actions. At β = 6.0, Wilson fermion results show clear finite size effects on the 83 × 16 lattice.  相似文献   

9.
We study the width of the confining string between static quarks in abelian lattice gauge theories using strong coupling expansions. We consider gauge groups Zn and U(1) in 3 and 4 dimensions. This extends previous work with Lüscher, where SU(2) and Z2 were studied. In ν = 3 dimensions we find evidence for a roughening transition. It is characterized by a divergence of the string width for an infinitely far separated quark-antiquark pair, while the string tension remains non-zero. In ν = 4 dimensions for the abelian groups we do not have evidence for a roughening transition away from a phase transition.  相似文献   

10.
We estimate the string tension by looking at Wilson loops and measuring the correlation between Wilson lines at g2 = 1.0 for lattice SU(3). The bound ΛLσ?0.0087 ± 0.0011 is larger than the previous results. The mass of the 0++ glueball is also estimated. The finite size effects on these quantities are shown to be large by comparing results on a 63 × 10 lattice with those on 94 lattice.  相似文献   

11.
Wilson loops inSU(2) lattice gauge theory without fermions are determined on lattices of size 124, 164 and 244 at β=2.4, 2.5 and 2.6. At β=2.6 the static quark-antiquark potential is extracted for distances up to 8 lattice units. A string tension smaller by a factor 2 than in previous investigations is found. Deviations from asymptotic scaling for multiplicatively improved Creutz ratios are certain, and their magnitude depends on the geometrical size of the ratios. This implies deviations from scaling.  相似文献   

12.
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.  相似文献   

13.
The reduced model à la Eguchi and Kawai, its quenched version and the Wilson theory in the string variable representation are studied by employing the loop expansion around the mean field. The spontaneous breakdown of the U(1)d symmetry in the Eguchi-Kawai model is thoroughly investigated. It is shown that the quenched reduced model undergoes the first-order phase transition in excellent agreement with the Monte Carlo data. The quenched reduced model is shown to be equivalent to the standard Wilson theory by comparing with the string variable Wilson theory at any finite order in the loop expansion in the large-N limit.  相似文献   

14.
Compact U(1) and SU(2) lattice gauge theories in 3 euclidean dimensions are studied by standard Monte Carlo techniques. The question of extracting reliable string tensions from these theories is examined in detail, including a comparison of the Monte Carlo Wilson loop data with weak coupling predictions and a careful error analysis: our conclusions are rather different from those of previous investigations of these theories. In the case of U(1) theory, we find that only a tiny range of β values can possibly be relevant for extracting a string tension and we are unable to convincingly demonstrate the expected exponential dependence of the string tension on β. For the SU(2) theory we are able to determine, albeit with rather large errors, a string tension from a study of Wilson loops.  相似文献   

15.
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17.
We use the linked cluster expansion methods of Nickel to derive strong couping series for ZN abelian gauge theories. These new results together with corresponding estimates using the exact linked cluster expansion algorithm are analysed and compared with previously obtained results for U(1) lattice gauge theory in 3 + 1 dimensions. We confirm the phase structure of these theories as found by other techniques. The critical value of N at which the phase structure of ZN alters is estimated to be NC = 4.5 ± 0.2. In each case the string tension estimates using the ELCE algorithm are found to be stable in the presence of a roughening transition.  相似文献   

18.
Wilson loops are calculated on 324 lattices in the coupling regime 6/g 2=6.3–6.9. Determination of the string tension from these loops with a method based on string model calculations shows a string tension that does not seem to scale. This is probably due to the amount of statistics. It points to difficulties in obtaining accurate physical results for coupling values above 6.6. Suggestions to improve this situation are made.  相似文献   

19.
We study the restoration of rotational symmetry of the heavy quark potential obtained from elongated planar and off-axis Wilson loops measured on a 164 lattice at β=5.4 and 5.7. While the rotational symmetry is still distorted at β=5.4 the potential is consistent with rotational symmetry at β=5.7. If we were in the asymptotic scaling region the linear slope would correspond at β=5.7 to a string tension ΛL/?σ = 0.0074±0.0002.  相似文献   

20.
《Physics letters. [Part B]》1988,205(4):535-539
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.  相似文献   

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