Overlap Fluctuations from Random Overlap Structures
نویسندگان
چکیده
We investigate overlap fluctuations of the Sherrington-Kirkpatrick mean field spin glass model in the framework of the Random Overlap Structure (ROSt). The concept of ROSt has been introduced recently by Aizenman and coworkers, who developed a variational approach to the Sherrington-Kirkpatrick model. We propose here an iterative procedure to show that, in the so-called Boltzmann ROSt, Aizenman-Contucci (AC) polynomials naturally arise for almost all values of the inverse temperature (not in average over some interval only). The same results can be obtained in any ROSt, including therefore the Parisi structure. The AC polynomials impose restrictions on the overlap fluctuations in agreement with Parisi theory. King’s College London, Department of Mathematics, Strand, London WC2R 2LS, United Kingdom, and Dipartimento di Fisica, Università di Roma “La Sapienza” Piazzale Aldo Moro 2, 00185 Roma, Italy, ICTP, Strada Costiera 11, 34014 Trieste, Italy,
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