Finite-Size Scaling Study of the Surface and Bulk Critical Behavior in the Random-Bond Eight-State Potts Model

Abstract

The self-dual random-bond eight-state Potts model is studied numerically through large-scale Monte Carlo simulations using the Swendsen-Wang cluster flipping algorithm. We compute bulk and surface order parameters and susceptibilities and deduce the corresponding critical exponents at the random fixed point using standard finite-size scaling techniques. The scaling laws are suitably satisfied. We can conclusively rule out that the model belongs to the 2D Ising model universality class. The dimensions of the relevant bulk and surface scaling fields are found to be ${y}_{h}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.849$, ${y}_{t}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.977$, and ${y}_{{h}_{s}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.54$, in contrast to their Ising values $15/8$, $1$, and $1/2$, respectively.