Dynamic critical properties of non-equilibrium Potts models with absorbing states

Abstract

We present extensive numerical simulations of a family of non-equilibrium Potts models with absorbing states that allows for a variety of scenarios, depending on the number of spin states and the range of the spin-spin interactions. These scenarios encompass a voter critical point, a discontinuous transition as well as the presence of both a symmetry-breaking phase transition and an absorbing phase transition. While we also investigate standard steady-state quantities, our emphasis is on time-dependent quantities that provide insights into the transient properties of the models.

Critical phenomena in presence of symmetric absorbing states: a microscopic spin model with tunable parameters

“…The expected voter critical behavior for this quantity (N f (t) ∼ t η GV with η GV = 0) suggests that N f (t) should be constant, and this has indeed been observed in a two-dimensional absorbing Ising model [22] as well as in linear voter models [23,35]. For our model, however, N f shows an early algebraic growth before it decreases as 1/ ln t at late times.…”

“…The scaling function f C only depends on the ratio of the two times t and s and decays algebraically for large arguments with an exponent λ. In [23] we showed that this aging scaling indeed prevails at a voter critical point, with the exponents taking on the values b = 0.120(5) and λ = 1.00 (2).…”

“…While this is formally compatible with η = 0, this behavior indicates that different scenarios are possible at a generalized voter critical point. As the number of cells whose cell magnetization density is not equal to −1 can be viewed as a proxy for the magnetization of a system formed by L 2 cells, we note that the logarithmic time dependence in Fig 3b is mirrored by a corresponding logarithmic behavior of the magnetization of non-linear models at their voter critical point [15,23,35]. In the inset of Fig.…”

“…There Previous efforts to verify these scenarios through microscopic spin models have only been partially successful, due to the lack of a microscopic spin model with parameters that can be changed continuously. Indeed, the best studied cases are that of absorbing Ising models on a square lattice with the added voter rule that a spin is not allowed to flip if it points in the same direction as all the spins in a specified neighborhood [19,22,23].…”

“…In numerical studies of kinetic Ising models [19,22,23] the different scenarios predicted by the Langevin equation are not found for a fixed range of the spin-spin interactions. Only when modifying the interaction range can one observe a change in scenario, with a unique generalized voter phase transition for nearest neighbor interactions and separate directed percolation and Ising phase transitions once the interaction distance exceeds a critical value.…”