Vesperini Arthur, Franzosi Roberto, Pettini Marco
Department of Physical Sciences, Earth and Environment (DSFTA), University of Siena, Via Roma 56, 53100 Siena, Italy.
INFN Sezione di Perugia, 06123 Perugia, Italy.
Entropy (Basel). 2025 Feb 28;27(3):258. doi: 10.3390/e27030258.
Resorting to microcanonical ensemble Monte Carlo simulations, we study the geometric and topological properties of the state space of a model of a network glass-former. This model, a Lennard-Jones binary mixture, does not crystallize due to frustration. We have found two peaks in specific heat at equilibrium and at low energy, corresponding to important changes in local ordering. These singularities were accompanied by inflection points in geometrical markers of the potential energy level sets-namely, the mean curvature, the dispersion of the principal curvatures, and the variance of the scalar curvature. Pinkall's and Overholt's theorems closely relate these quantities to the topological properties of the accessible state-space manifold. Thus, our analysis provides strong indications that the glass transition is associated with major changes in the topology of the energy level sets. This important result suggests that this phase transition can be understood through the topological theory of phase transitions.
通过采用微正则系综蒙特卡罗模拟，我们研究了网络玻璃形成体模型状态空间的几何和拓扑性质。该模型是一种 Lennard-Jones 二元混合物，由于受挫而不会结晶。我们在平衡态和低能量下的比热中发现了两个峰值，这对应于局部有序性的重要变化。这些奇点伴随着势能水平集几何标记中的拐点，即平均曲率、主曲率的离散度和标量曲率的方差。Pinkall 定理和 Overholt 定理将这些量与可及状态空间流形的拓扑性质紧密联系起来。因此，我们的分析有力地表明玻璃转变与能量水平集拓扑结构的重大变化有关。这一重要结果表明，这种相变可以通过相变的拓扑理论来理解。
