2 Method and Simulation

Interface tension in SU(3) lattice gauge theory at finite temperatures on an N t = 2 lattice The surface tension σ of the confined-deconfined interface is calculated in pure SU(3) lattice gauge theory at finite temperatures employing the operator and integral methods on a lattice of a size 8 2 × N z × 2 with N z = 16 and 40. Analyses of non-perturbative corrections in asymmetry response functions strongly indicate that the use of one-loop values for the response functions lead to an overestimate of σ in the operator method. The operator method also suffers more from finite-size effects due to a finite thickness of the interface, leading us to conclude that the integral method yields more reliable values for σ. Our result with the integral method σ/T 3 c = 0.134(16) is consistent with earlier results and also with that obtained with a transfer matrix method. Result is also reported on σ obtained on a lattice 18 2 ×48×4 with the integral method. Numerical simulation of pure SU(3) gauge system on a lattice has shown that the system undergoes a first order phase transition from a confined phase at low temperatures to a deconfined phase at high temperatures [1]. The two phases can therefore coexist at the transition temperature T c , separated by an interface. A basic parameter characterizing the interface is the interface tension σ. A number of numerical work has recently been carried out to determine its value, mainly for a system with the temporal lattice size N t = 2. Kajantie, Kärkkäinen and Rummukainen[2, 3] developed an operator method for measuring the tension and reported the value σ/T 3 c = 0.24(6) for N t = 2[3]. Independently, Potvin and Rebbi[4] proposed to employ an integral of the derivative of the free energy in the parameter space of the coupling constant to measure the tension, and found σ/T 3 c = 0.115(13) for the same temporal lattice size[5]. A factor two discrepancy between these results has motivated further studies of the interface[6, 7, 8, 9], which yielded values of σ/T 3 c similar to that of the integral method. The method of histograms[10] and the technique of transfer matrix[6] used in these studies are quite different, however, from the operator and the integral method. Hence the discrepancy of the original results obtained with the two methods has not been resolved. In this article …