Europhys. Lett.
Volume 75, Number 3, August 2006
Page(s) 385 - 391
Section General
Published online 21 June 2006
Europhys. Lett., 75 (3), pp. 385-391 (2006)
DOI: 10.1209/epl/i2006-10120-y

Local spin glass order in 1D

S. 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.

© EDP Sciences 2006