Finite Size Scaling and Universality in SU(2) at Finite Temperature

Abstract

We study the 4-th Binder cumulant on $4\times {N_{\sigma }}^3$ lattices for a pure SU(2) gauge theory. We use 20 data points for a sequence of $N_{\sigma }$ in $\beta$ intervals shrinking when $N_{\sigma }$ increases, in order to reduce the nonlinear effects. Using a log-log fit of the slope versus $N_{\sigma }$, we obtain the preliminary result $\nu =0.637(11)$ in reasonably good agreement with the value for the 3D Ising model universality class. The corrections due to irrelevant directions appear to be dominated by a term proportional to ${N_{\sigma }}^{-2.03(4)}$ which seems compatible with the breaking of rotational symmetry.

Comments: 7 pages, 5 figures, Poster presented at the "XXVII International Symposium on Lattice Field Theory", July 26-31 2009, Peking University, Beijing, China