论文标题
微域相变的分析中的几何方面
Geometrical aspects in the analysis of microcanonical phase-transitions
论文作者
论文摘要
在目前的工作中，我们讨论了如何从相位空间子集的几何特性中推导热力学可观察物的功能形式。考虑的几何量主要是正在研究的系统的哈密顿量的能级集的外部曲率。特别是，事实证明，相变点的热力学可观察物的特殊行为植根于相位空间中能级集的几何形状的更根本变化。更具体地说，我们讨论了如何在$ ϕ^4 $模型的特殊情况下形成相位转换的微域和几何描述，该模型具有最近的neighbours和均值场相互作用。
In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the energy level sets of the Hamiltonian of a system under investigation. In particular, it turns out that peculiar behaviours of thermodynamic observables at a phase transition point are rooted in more fundamental changes of the geometry of the energy level sets in phase space. More specifically, we discuss how microcanonical and geometrical descriptions of phase-transitions are shaped in the special case of $ϕ^4$ models with either nearest-neighbours and mean-field interactions.
