论文标题
Ising模型淬火中的静态和动态之间的关系到临界点以下
Relation between Statics and Dynamics in the Quench of the Ising Model to below the Critical Point
论文作者
论文摘要
标准的相位顺序过程是通过将像ISING模型这样的系统淬灭到临界点以下的系统获得。这通常是在周期性的边界条件下进行的，以确保在低温阶段破裂。通过这种布置，无限系统已知将永久脱离平衡，即存在一个明确定义的渐近状态，该状态是时间不变的，但与有序的铁磁状态不同。在本文中，我们通过数字证明具有周期性和反碘边界条件的淬灭动力学是无法区分的，从而确定了这种不变状态的批判性质。然而，尽管渐近状态与周期案例的平衡状态不一致，但它与反碘病例的平衡状态相吻合，实际上这很重要。 ISING模型的具体例子被证明是一个更通用现象的实例，因为在球形模型中出现了类似的图片，其中边界条件将固定在周期性上，而脱节或保留麦格牙性是通过敏锐或平稳地施加球形约束或平滑来管理的。
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.
