Topological origin of the phase transition in a mean-field model

被引:39
|
作者
Casetti, L
Cohen, EGD
Pettini, M
机构
[1] Politecn Torino, Dipartimento Fis, Unita Ricerca, Ist Nazl Fis Mat, I-10129 Turin, Italy
[2] Rockefeller Univ, New York, NY 10021 USA
[3] Osserv Astrofis Arcetri, I-50125 Florence, Italy
[4] Ist Nazl Fis Mat, Unita Ricerca Firenze, Florence, Italy
[5] Ist Nazl Fis Nucl, Sezione Firenze, I-50125 Florence, Italy
关键词
D O I
10.1103/PhysRevLett.82.4160
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We argue that the phase transition in the mean-field XY model is related to a particular change in the topology of its configuration space. The nature of this topological change can be discussed on the basis of elementary Morse theory using the potential energy per particle V as a Morse function. The value of V where such a topological change occurs equals the thermodynamic value of V at the phase transition and the number of (Morse) critical points grows very fast with the number of particles N. Furthermore, as in statistical mechanics, the way the thermodynamic limit is taken is crucial in topology. [S0031-9007(99)09249-2].
引用
收藏
页码:4160 / 4163
页数:4
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