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Some comments on the connection between disordered long range spin glass models and their mean field version

Francesco Guerra1 and Fabio Lucio Toninelli2

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In this paper, we consider a particular aspect of the relationship between mean field and finite-dimensional spin glasses. By means of a simple interpolation method, we prove that the free energy of a class of finite-dimensional spin glass models with Kac-type interactions is bounded below by that of their mean field analogue. As a result, Parisi theory of replica symmetry breaking can be exploited in order to give bounds on their free energy and ground state energy. Similar results hold for diluted versions of the systems.


PACS

75.10.Nr Spin-glass and other random models

02.60.Ed Interpolation; curve fitting

MSC

82D30 Random media, disordered materials (including liquid crystals and spin glasses)

Subjects

Computational physics

Condensed matter: electrical, magnetic and optical

Dates

Issue 43 (31 October 2003)

Received 11 June 2003

Published 15 October 2003



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