Monte Carlo technique for universal finite-size-scaling functions: Application to the 3-state Potts model on a square lattice

We present a method which allows calculation of whole universal finite-size-scaling functions from Monte Carlo data. The crux of the new method is a technique of isolating the singular part from the total free energy. We apply this method to the 3-state Potts model on a square lattice and find the normalized scaling function Y(x) in the form 1+x+5.31${\mathit{x}}^2$-1.2${\mathit{x}}^3$-0.67${\mathit{x}}^4$ . . . near the bulk critical point x=0, together with the normalizing universal amplitude E=1.053 and a nonuniversal metric factor D=-0.387. It also behaves as Y(x)≊(±x${)}^{\mathit{d}\nu }$ ${\mathit{Q}}_{\pm }$ for large x in agreement with the hyperuniversality hypothesis with ${\mathit{Q}}_{+}$/${\mathit{Q}}_{\mathrm{-}}$≊1.