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We discuss a phase transition in spin glass models which have been rarelyconsidered in the past, namely the phase transition that may take place whentwo real replicas are forced to be at a larger distance (i.e. at a smalleroverlap) than the typical one. In the first part of the work, by solvinganalytically the Sherrington-Kirkpatrick model in a field close to its criticalpoint, we show that even in a paramagnetic phase the forcing of two realreplicas to an overlap small enough leads the model to a phase transition wherethe symmetry between replicas is spontaneously broken. More importantly, thisphase transition is related to the de Almeida-Thouless (dAT) critical line. Inthe second part of the work, we exploit the phase transition in the overlapbetween two real replicas to identify the critical line in a field infinite-dimensional spin glasses. This is a notoriously difficult computationalproblem, because of huge finite-size corrections. We introduce a new method ofanalysis of Monte Carlo data for disordered systems, where the overlap betweentwo real replicas is used as a conditioning variate. We apply this analysis toequilibrium measurements collected in the paramagnetic phase in a field, $h>0$and $T_c(h)<T<T_c(h=0)$, of the $d=1$ spin glass model with long-rangeinteractions decaying fast enough to be outside the regime of validity of themean-field theory. We thus provide very reliable estimates for thethermodynamic critical temperature in a field.

entropy

Spin glasses in a field show a phase transition varying the distance  among real replicas (and how to exploit it to find the critical line in a  field)