IFAC-CNR Institute of Applied Physics "Nello Carrara", Via Madonna del Piano 10, I-50019 Sesto Fiorentino (FI), Italy.
Phys Rev E. 2019 Jul;100(1-1):012124. doi: 10.1103/PhysRevE.100.012124.
In this paper we present the study of the topology of the equipotential hypersurfaces of configuration space of the mean-field ϕ^{4} model with a Z_{2} symmetry. Our purpose is discovering, if any, the relation between the second-order Z_{2}-symmetry-breaking phase transition and the geometric entities mentioned above. The mean-field interaction allows us to solve analytically either the thermodynamic in the canonical ensemble or the topology by means of Morse theory. We have analyzed the results in the light of two theorems on sufficiency conditions for symmetry-breaking phase transitions recently proven. This study is part of a research line based on the general framework of geometric-topological approach to Hamiltonian chaos and critical phenomena.
在本文中，我们研究了具有 Z_{2} 对称性的平均场 ϕ^{4} 模型的位形空间等位面的拓扑结构。我们的目的是发现，如果有的话，二阶 Z_{2}-对称破缺相变与上述几何实体之间的关系。平均场相互作用允许我们通过 Morse 理论解析地求解正则系综中的热力学或拓扑。我们根据最近证明的两个关于对称破缺相变充分条件的定理来分析结果。这项研究是基于哈密顿混沌和临界现象的几何拓扑方法的一般框架的研究的一部分。
