# Effective actions for finite temperature Lattice Gauge Theories

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Michele Caselle, Sep 03, 2013 Available from:- References (3)
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**ABSTRACT:**The connection between euclidean and hamiltonian lattice QCD requires the use of asymmetric lattices, which in turn implies the necessity of two coupling parameters. We analyse the dependence of space- and time-like couplings gσ and gτ on the different lattice spacings a and aτ in space and time directions. Using the background field method we determine the derivatives of the couplings with respect to the asymmetry factor in the weak coupling limit, obtaining for ξ=1 the values. We argue that the sum of these derivatives has to be equal to b0=11N/48π2 and determine the Λ parameter for asymmetric lattices. In the limit ξ→∞ all our results agree with those of A. and P. Hasenfratz.Nuclear Physics B 05/1982; 205(2-205):285-300. DOI:10.1016/0550-3213(82)90390-X · 3.95 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We determine the critical couplings for the deconfinement phase transition in SU(2) gauge theory on Nτ × Nσ3 lattices with Nτ = 8 and 16 and Nσ varying between 16 and 48. A comparison with string tension data shows scaling of the ratio Tc/√σ in the entire coupling regime ß = 2.30−2.75, while the individual quantities still exhibit large scaling violations. We find Tc/√σ = 0.69(2). We also discuss in detail the extrapolation of to the continuum limit. Our result, which is consistent with the above ratio, is and . We also comment upon corresponding results for SU(3) gauge theory and four-flavour QCD.Nuclear Physics B 03/1993; 30(2-392):493-517. DOI:10.1016/0550-3213(93)90682-F · 3.95 Impact Factor -
##### Article: Toward an analytic determination of the deconfinement temperature in SU(2) lattice gauge theory

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**ABSTRACT:**We consider the SU(2) lattice gauge theory at finite temperature in (d+1) dimensions, with different couplings βt and βs for time-like and space-like plaquettes. By using the character expansion of the Wilson action and performing the integrals over space-like link variables, we find an effective action for the Polyakov loops which is exact to all orders inβt and to the first non-trivial order in βs.The critical coupling for the deconfinement transition is determined in the (3+1)-dimensional case, by the mean field method, for different values of the lattice size Nt in the compactified time direction and of the asymmetry parameter ϱ = √βt/βs. We find a remarkable improvement in the results compared to the zeroth-order approximation in βs, leading to a reasonably good numerical agreement with the Monte Carlo simulations in the range 1 ⩽Nt5. Moreover the dependence of the results on the parameter ϱ is in excellent agreement with previous theoretical predictions.Nuclear Physics B 07/1996; 472(1-2-472):163-193. DOI:10.1016/0550-3213(96)00223-4 · 3.95 Impact Factor