Three-dimensional finite temperature Z$_2$ gauge theory with tensor network scheme

Abstract: We apply a tensor network scheme to finite temperature Z$2$ gauge theory in 2+1 dimensions. Finite size scaling analysis with the spatial extension up to $N{\sigma}=4096$ at the temporal extension of $N_\tau=2,3,5$ allows us to determine the transition temperature and the critical exponent $\nu$ at high level of precision, which shows the consistency with the Svetitsky-Yaffe conjecture.