Integer Optimization and Zero-Temperature Fixed Point in Ising Random-Field Systems

Abstract

Phase transition in $d=3\mathrm{}$ ferromagnetic Ising models with random fields is analyzed directly at the zero-temperature critical point. Critical behavior is extracted from correlation functions averaged over an ensemble of exact ground states obtained with a new integer optimization algorithm. For Gaussian distribution of random fields finite-size scaling demonstrates a continuous phase transition with effective disconnected susceptibility exponent $\tilde{\eta }\approx -0.9\mathrm{}$, correlation-length exponent $\nu \approx 1.0$, and magnetization exponent $\beta \approx 0.05$.