Francesco Guerra and Fabio Lucio Toninelli 2003 J. Phys. A: Math. Gen. 36 10987 doi:10.1088/0305-4470/36/43/022
Francesco Guerra1 and Fabio Lucio Toninelli2
Show affiliationsIn 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.
82D30 Random media, disordered materials (including liquid crystals and spin glasses)
Issue 43 (31 October 2003)
Received 11 June 2003
Published 15 October 2003
Francesco Guerra and Fabio Lucio Toninelli 2003 J. Phys. A: Math. Gen. 36 10987
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