Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2010-10-05
JHEP 1102:057,2011
Physics
High Energy Physics
High Energy Physics - Lattice
27 pages, 21 figures; final version published in JHEP; attached the corresponding Erratum (ref. JHEP 1107:014,2011, DOI 10.100
Scientific paper
10.1007/JHEP02(2011)057
We derive three-dimensional, Z(N)-symmetric effective actions in terms of Polyakov loops by means of strong coupling expansions, starting from thermal SU(N) Yang-Mills theory in four dimensions on the lattice. An earlier action in the literature, corresponding to the (spatial) strong coupling limit, is thus extended by several higher orders, as well as by additional interaction terms. We provide analytic mappings between the couplings of the effective theory and the parameters $N_\tau,\beta$ of the original thermal lattice theory, which can be systematically improved. We then investigate the deconfinement transition for the cases SU(2) and SU(3) by means of Monte Carlo simulations of the effective theory. Our effective models correctly reproduce second order 3d Ising and first order phase transitions, respectively. Furthermore, we calculate the critical couplings $\beta_c(N_\tau)$ and find agreement with results from simulations of the 4d theory at the few percent level for $N_\tau=4-16$.
Langelage Jens
Lottini Stefano
Philipsen Owe
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