Phase transitions in a disordered system in and out of equilibrium

TL;DR

This paper compares equilibrium and non-equilibrium phase transitions in the disordered RFIM, identifying the demagnetized state as the non-equilibrium counterpart to the ground state and providing evidence of universality across different conditions.

Contribution

It demonstrates that the demagnetized state serves as the correct non-equilibrium analogue to the ground state and shows universality in critical behavior between equilibrium and non-equilibrium phases.

Findings

Exponents and scaling functions coincide in 3D simulations.

Critical point locations differ between states.

Results are relevant for optimization and universality in disordered systems.

Abstract

The equilibrium and non--equilibrium disorder induced phase transitions are compared in the random-field Ising model (RFIM). We identify in the demagnetized state (DS) the correct non-equilibrium hysteretic counterpart of the T=0 ground state (GS), and present evidence of universality. Numerical simulations in d=3 indicate that exponents and scaling functions coincide, while the location of the critical point differs, as corroborated by exact results for the Bethe lattice. These results are of relevance for optimization, and for the generic question of universality in the presence of disorder.