J. F. Fernández, J. J. Alonso
We extract a pair correlation function (PCF) from probability distributions of the spin-overlap parameter q. The distributions come from Monte Carlo simulations. A measure, w, of the thermal fluctuations of magnetic patterns follows from the PCFs. We also obtain rms deviations (over different system samples) delta_p away from average probabilities for q. For the linear system-sizes $L$ we have studied, (i) w and delta_p are independent of L in the Edwards-Anderson model but scale as 1/L and sqrt{L}, respectively, in the Sherrington-Kirkpatrik model.
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http://arxiv.org/abs/1207.4008
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