Metastability of Universality Classes

Denis Gessert, Martin Weigel, Wolfhard Janke E

We study the Ising model with competing ferromagnetic nearest- and antiferromagnetic next-nearest-neighbor interactions of strengths J 1 > 0 and J 2 < 0 , respectively, on the honeycomb lattice. For J 2 > − J 1 / 4 it has a ferromagnetic ground state, and previous work has shown that at least for J 2 ≳ − 0.2 J 1 the transition is in the Ising universality class. For even lower J 2 some indicators pointing towards a first-order transition were reported. By utilizing population annealing Monte Carlo simulations together with a rejection-free and adaptive update, we can equilibrate systems with J 2 as low as − 0.23 J 1 . By means of a finite-size scaling analysis we show that the system undergoes a second-order phase transition within the Ising universality class at least down to J 2 = − 0.23 J 1 and, most likely, for all J 2 > − J 1 / 4 . As we show here, there exist very long-lived metastable states in this system explaining the first-order like behavior seen in only partially equilibrated systems.

Prabodh Shukla, Nenad M. Svrakic

Ole Peters, Michelle Girvan

Ivan Balog, Matthieu Tissier, Gilles Tarjus

The random-field Ising model (RFIM) is one of the simplest statistical-mechanical models that captures the anomalous irreversible collective response seen in a wide range of physical, biological, or socioeconomic situations in the presence of interactions and intrinsic heterogeneity or disorder. When slowly driven at zero temperature, it can display an out-of-equilibrium phase transition associated with critical scaling (``crackling noise''), while it undergoes at equilibrium, under either temperature or disorder-strength changes, a thermodynamic phase transition. We show that the out-of-equilibrium and equilibrium critical behaviors are in the same universality class: they are controlled, in the renormalization-group (RG) sense, by the same zero-temperature fixed point. We do so by combining a field-theoretical formalism that accounts for the multiple metastable states and the exact (functional) RG. As a spin-off, we also demonstrate that critical fluids in disordered porous media are in the same universality class as the RFIM, thereby unifying a broad spectrum of equilibrium and out-of-equilibrium phenomena.