High-degeneracy Potts coarsening

Abstract

I examine the fate of a kinetic Potts ferromagnet with a high ground-state degeneracy that undergoes a deep quench to zero temperature. I consider single spin-flip dynamics on triangular lattices of linear dimension 8 L 128 and set the number of spin states q equal to the number of lattice sites L × L. The ground state is the most abundant final state, and is reached with probability ≈0.71. Three-hexagon states occur with probability ≈0.26, and hexagonal tessellations with more than three clusters form with probabilities of O(10 −3 ) or less. Spanning stripe states-where the domain walls run along one of the three lattice directions-appear with probability ≈0.03. "Blinker" configurations, which contain perpetually flippable spins, also emerge, but with a probability that is vanishingly small with the system size.

Low-temperature universal dynamics of the bidimensional Potts model in the large q limit

“…2 for the square geometry. These are typical blocked states at zero temperature, as the ones studied in [44,[48][49][50]. After a T /T c dependent time-scale needed to escape such states, the system enters the proper dynamic scaling regime that takes it towards equilibrium.…”

“…It is of the order of a few δ (concretely, 3.63 δ for q → ∞ on the square lattice) and it very weakly depends on q and T /T c . The triangular lattice model does not show this kind of blocking (see also [45,50]). Therefore, we conclude that, in quenches to T /T c ≤ 1/2, after a short transient, the large q Potts model reaches a state of the kind of the blocked configurations at zero temperature on the square and honeycomb lattices, while it progressively orders with no arrest on the triangular lattice.…”

“…In short, we study the dynamical behaviour after a rapid quench for sufficiently large q so that the transition is of first order. While curvature driven coarsening should be the leading mechanism for ordering [39][40][41][42][43][44], the Potts model dynamics also present low temperature freezing [45][46][47][48][49][50] and metastability close to the critical temperature [38,[51][52][53][54][55] that may conspire against the system reaching equilibrium after the quench. In both works we aim to improve our understanding of the interplay between the coarsening process, the low temperature freezing and the metastability close to criticality.…”

How many phases nucleate in the bidimensional Potts model?

“…In the following we will consider a protocol in which the system, initially prepared in an infinite temperature equilibrium state, is suddenly quenched at time t = 0 to a low temperature T < Tc. The dynamical evolution has been studied in previous works [35][36][37][38][39][40][41][42][43][44][45][46] mainly focusing on the coarsening regime. Here we are more interested in metastability and multi-nucleation, which clearly arise at T Tc.…”

“…Phases which do not nucleate disappear from the system immediately after the metastable state is escaped. Those which nucleate start competing, resulting in a coarsening process [35][36][37][38][39][40][41][42][43][44][45][46] which leads, at some point, to the progressive elimination of the less represented colours until symmetry is definitively broken, one single colour survives, and equilibrium is attained (at not too low temperatures; otherwise, blocked states of the kind discussed in [35][36][37][38][39][40] can stop the evolution).…”