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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 |
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| Cite this article: |
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TIAN Guangshan 1991 Chin. Phys. Lett. 8 263-266 |
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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.
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| Keywords:
75.10.Nr
64.60.Cn
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Published: 01 May 1991
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| PACS: |
75.10.Nr
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(Spin-glass and other random models)
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64.60.Cn
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(Order-disorder transformations)
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