Critical exponents testing of a random number generator with the Wolff cluster algorithm

Abstract

Finite-size scaling (FSS) of critical exponents including γ, β and α of 2D Ising models of sizes up to 327682 are studied using the Wolff clustering algorithm and are used to assess the quality of pseudorandom number generators (PRNGs). Critical exponents of PRNGs with quality issues are found to diverge from their theoretical values at large lattice sizes, similar to previous reports that used the Metropolis algorithm to simulate the Ising lattice. Four high-quality PRNGs, including Mersenne Twister, an additive lagged Fibonacci generator, Xorshift and Xorwow are tested and assessed with their FSS behaviors. Dynamic exponent z is also used to assess the quality of the four tested PRNGs and corroborating results are obtained.