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

We study the 4-th Binder cumulant on $4\times{N_σ}^3$ lattices for a pure SU(2) gauge theory. We use 20 data points for a sequence of ${N_σ}$ in $β$ intervals shrinking when ${N_σ}$ increases, in order to reduce the nonlinear effects. Using a log-log fit of the slope versus ${N_σ}$, we obtain the preliminary result $ν=0.637(11)$ 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 ${N_σ}^{-2.03(4)}$ which seems compatible with the breaking of rotational symmetry.

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