平均场自旋玻璃模型：熵方法(英文)

Mean field spin glass model:an entropy approach

定义一个μ(X)=1的有限测度空间(X,μ),引入在(X,μ)上的一个态函数的平均场自旋玻璃模型.考察了该模型的基本性质,并研究该模型的自由能和态函数上的熵之间的关系.研究表明:在高温情形下,该模型满足熵最大化原理,即对给定的较小(逆)温,当态函数达到最大值lg2时,该模型的自由能达到最大.

Let（X,μ） be a finite measure space with μ（X）=1.In this paper a mean field spin glass model associated with a state function  on（X,μ） is introduced.The basic properties of the model and relationship between the（limit） free energy of the model and the entropy of the state function  are studied.The results show that in the case of high temperature the model satisfies the maximum entropy principle：for fixed small inverse temperature,the（limit）free energy of the model achieves its maximum when the state function  has the maximum entropy lg2.