Relation between Statics and Dynamics in the Quench of the Ising Model to below the Critical Point
| Autor: | Marco Zannetti, Antonio Coniglio, Annalisa Fierro |
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| Rok vydání: | 2020 |
| Předmět: |
Physics
Statistical Mechanics (cond-mat.stat-mech) Thermodynamic equilibrium Ergodicity FOS: Physical sciences Invariant (physics) 01 natural sciences 010305 fluids & plasmas Spherical model Critical point (thermodynamics) 0103 physical sciences Periodic boundary conditions Ising model Boundary value problem Statistical physics 010306 general physics Condensed Matter - Statistical Mechanics |
| DOI: | 10.48550/arxiv.2006.16914 |
| Popis: | The standard phase-ordering process is obtained by quenching a system, like the Ising model, to below the critical point. This is usually done with periodic boundary conditions to insure ergodicity breaking in the low temperature phase. With this arrangement the infinite system is known to remain permanently out of equilibrium, i.e. there exists a well defined asymptotic state which is time-invariant but different from the ordered ferromagnetic state. In this paper we establish the critical nature of this invariant state, by demonstrating numerically that the quench dynamics with periodic and antiperiodic boundary conditions are indistinguishable one from the other. However while the asymptotic state does not coincide with the equilibrium state for the periodic case, it coincides instead with the equilibrium state of the antiperiodic case, which in fact is critical. The specific example of the Ising model is shown to be one instance of a more general phenomenon, since an analogous picture emerges in the spherical model, where boundary conditions are kept fixed to periodic, while the breaking or preserving of ergodicity is managed by imposing the spherical constraint either sharply or smoothly. Comment: 18 pages, 9 figures |
| Databáze: | OpenAIRE |
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