Critical Ising system testing of high-quality random number generators

Abstract

Specialized hardware implemented on field programmable gate array (FPGA) is used to simulate critical 2D Ising lattices up to 40962. Four mainstream, high-quality pseudorandom number generators (PRNGs) including Xorshift, Mersenne Twister, Xorwow, and ALFG are tested on this system, and three of them are found to misbehave with different degree of confidence levels. It is observed that PRNGs with quality issues tend to misbehave in critical Ising systems and the ones with bigger issues start to misbehave in smaller critical Ising systems and vice versa. The size at which a PRNG misbehaves is proposed as a measure of a PRNG’s quality.