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< Conference on Computational Physics
02/05/2023 - Age: 1 year

Paper on percolation in spin glasses

Manuscript selected as Editors' Suggestion

In work with our student Lambert MĂĽnster that has just been published in Physical Review E as an Editors' Suggestion, we explored possible avenues towards a description of the spin-glass transition in terms of a geometrical percolation phenomenon. Such a picture which is well established for standard magnetic ordering phenomena, has been elusive since long for the case of systems with frustrating disorder. Based on careful simulations in two dimensions we test the behavior of several candidate cluster types constructed on the basis of two replica of the system and show that their percolation transitions remain distinct from the spin-glass transition.

Here is the full abstract:

Suitable cluster definitions have allowed researchers to describe many ordering transitions in spin systems as geometric phenomena related to percolation. For spin glasses and some other systems with quenched disorder, however, such a connection has not been fully established, and the numerical evidence remains incomplete. Here we use Monte Carlo simulations to study the percolation properties of several classes of clusters occurring in the Edwards-Anderson Ising spin-glass model in two dimensions. The Fortuin-Kasteleyn–Coniglio-Klein clusters originally defined for the ferromagnetic problem do percolate at a temperature that remains nonzero in the thermodynamic limit. On the Nishimori line, this location is accurately predicted by an argument due to Yamaguchi. More relevant for the spin-glass transition are clusters defined on the basis of the overlap of several replicas. We show that various such cluster types have percolation thresholds that shift to lower temperatures by increasing the system size, in agreement with the zero-temperature spin-glass transition in two dimensions. The overlap is linked to the difference in density of the two largest clusters, thus supporting a picture where the spin-glass transition corresponds to an emergent density difference of the two largest clusters inside the percolating phase.