The Pseudo Specific Heat in SU(2) Gauge Theory : Finite Size Dependence and Finite Temperature Effects

Abstract

We investigate the pseudo specific heat of SU(2) gauge theory near the crossover point on $4^4$ to $16^4$ lattices. Several different methods are used to determine the specific heat. The curious finite size dependence of the peak maximum is explained from the interplay of the crossover phenomenon with the deconfinement transition occurring due to the finite extension of the lattice. We find, that for lattices of size $8^4$ and larger the crossover peak is independent of lattice size at ${\beta }_{co}=2.23(2)$ and has a peak height of $C_{V,co}=1.685(10)$. We conclude therefore that the crossover peak is not the result of an ordinary phase transition. Further, the contributions to $C_V$ from different plaquette correlations are calculated. We find, that at the peak and far outside the peak the ratio of contributions from orthogonal and parallel plaquette correlations is different. To estimate the finite temperature influence on symmetric lattices far off the deconfinement transition point we calculate the modulus of the lattice average of the Polyakov loop on these lattices and compare it to predictions from a random walk model.

Comments: Latex 2e,10 pages including 5 postscript figures