Thermodynamic glass transition: seeking for statistical mechanical models and extracting their characteristics

为了实现理想玻璃的最终目标，分子在平衡状态下以不规则的方式冻结，我们在平衡统计力学的框架内分析了各种数学模型，这些模型将原子能级描述与物质的宏观状态联系起来。结果，我们发现了一个有限维模型，它显示了宏观重叠的出现。虽然这个模型的跃迁似乎是有潜热的一级跃迁，但我们也发现了另一个没有潜热的随机一级跃迁模型。这两个结果是世界上的第一个报告，它们将为深入理解逼真眼镜提供重要的一步。

Toward the ultimate goal to have "ideal glass", in which molecules are frozen in an irregular manner at equilibrium, we have analyzed various mathematical models within a framework of equilibrium statistical mechanics that connect atomic level descriptions with macroscopic states of matter. As the result, we have found a finite dimensional model that exhibits the emergence of macroscopic overlap. While the transition of this model seems to be of the first-order with latent heat, we also find another model that exhibits Random First Order Transition without latent heat. These two results are the first report in the world, and they will provide a significant step toward deep understanding of realistic glasses.