Upper and Lower Bounds to the Free Energy Density of a One-dimensional Spin Glass Model
TIAN Guangshan
Department of Physics, Peking University, Beijing 100871
Upper and Lower Bounds to the Free Energy Density of a One-dimensional Spin Glass Model
TIAN Guangshan
Department of Physics, Peking University, Beijing 100871
关键词 ：
75.10.Nr ,
64.60.Cn
Abstract ： In this paper, a one-dimensional short-ranged spin-glass model in a random magnetic field is studied. Noticing convexity of the partition function, we use Jensen's inequality to obtain a lower bound to the averaged free energy density and the slope inequality for an upper bound. These bounds are derived under very general conditions and they can be used as tests for various approximate methods such as the replica method.
Key words ：
75.10.Nr
64.60.Cn
出版日期: 1991-05-01
:
75.10.Nr
(Spin-glass and other random models)
64.60.Cn
(Order-disorder transformations)
引用本文:
TIAN Guangshan. Upper and Lower Bounds to the Free Energy Density of a One-dimensional Spin Glass Model[J]. 中国物理快报, 1991, 8(5): 263-266.
链接本文:
https://cpl.iphy.ac.cn/CN/
或
https://cpl.iphy.ac.cn/CN/Y1991/V8/I5/263
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1991, Vol. 8 
