关于相变拓扑理论的明显失效
On the apparent failure of the topological theory of phase transitions
摘要：
相变的拓扑理论有其优点，在两个定理证明，对于广泛的一类物理系统，相变必然源于拓扑变化的一些子流形的配置空间。最近有人认为，$2D$格$ϕ^4$ -模型提供了一个反例，证伪这一理论。它在这里示出，这是不是这样的情况下：该模型的相变源于渐近（$N\to\infty$）的拓扑结构的变化的能级集，尽管没有临界点的潜力对应的过渡能量。
英文摘要：
The topological theory of phase transitions has its strong point in two theorems proving that, for a wide class of physical systems, phase transitions necessarily stem from topological changes of some submanifolds of configuration space. It has been recently argued that the $2D$ lattice $ϕ^4$-model provides a counterexample that falsifies this theory. It is here shown that this is not the case: the phase transition of this model stems from an asymptotic ($N\to\infty$) change of topology of the energy level sets, in spite of the absence of critical points of the potential in correspondence of the transition energy.
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