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J Chem Phys. 2011 Jan 21;134(3):034513. doi: 10.1063/1.3506843.
There are deep analogies between the melting dynamics in systems with a first-order phase transition and the dynamics from equilibrium in super-cooled liquids. For a class of Ising spin models undergoing a first-order transition--namely p-spin models on the so-called Nishimori line--it can be shown that the melting dynamics can be exactly mapped to the equilibrium dynamics. In this mapping the dynamical--or mode-coupling--glass transition corresponds to the spinodal point, while the Kauzmann transition corresponds to the first-order phase transition itself. Both in mean field and finite dimensional models this mapping provides an exact realization of the random first-order theory scenario for the glass transition. The corresponding glassy phenomenology can then be understood in the framework of a standard first-order phase transition.
在具有一级相变的系统中的熔化动力学和过冷液体的平衡动力学之间存在深刻的相似性。对于一类经历一级相变的伊辛自旋模型——即在所谓的 Nishimori 线上的 p-自旋模型——可以证明熔化动力学可以精确地映射到平衡动力学。在这种映射中，动力学——或模式耦合——玻璃转变对应于 spinodal 点，而 Kauzmann 转变对应于一级相变本身。在平均场和有限维模型中，这种映射为玻璃转变的随机一级理论情景提供了一个精确的实现。然后，可以在标准一级相变的框架内理解相应的玻璃现象学。
