Local spin glass order in 1DS. Franz1, 2 and G. Parisi3, 4
1 The Abdus Salam International Centre for Theoretical Physics Strada Costiera 11, P.O. Box 586, I-34100 Trieste, Italy
2 Isaac Newton Institute for Mathematical Sciences 20 Clarkson Road, Cambridge, CB3 0EH, UK
3 Dipartimento di Fisica, Università di Roma "La Sapienza" P.le A. Moro 2, 00185 Roma, Italy
4 INFM - CRS SMC, INFN, Università di Roma "La Sapienza" P.le A. Moro 2, 00185 Roma, Italy
received 19 April 2006; accepted 2 June 2006
published online 21 June 2006
We study the behavior of one-dimensional Kac spin glasses as a function of the interaction range. We verify by Monte Carlo numerical simulations the crossover from local mean-field behavior to global paramagnetism. We investigate the behavior of correlations and find that in the low-temperature phase correlations grow at a faster rate then the interaction range. We completely characterize the growth of correlations in the vicinity of the mean-field critical region.
05.20.-y - Classical statistical mechanics.
75.10.Nr - Spin-glass and other random models.
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