Ground State Properties of the Diluted Sherrington-Kirkpatrick Spin Glass

In a numerical study of dilute versions of the Sherrington-Kirkpatrick mean-field spin glass at temperature T=0, we approximate the energies of ground states of ensembles at variable dilution with high accuracy using the Extremal Optimization heuristic [1,2]. We find that the scaling properties of such systems possess exponents that are parametrized by the degree of dilution [3,4]. This is a surprising result, as one would not expect that gradual bond-dilution would continuously change the universality class of a statistical model. (There is no evidence of a percolation transition separating a trivially disconnected regime from a percolation regime, as one might expect.) It may open the door to a perturbative study of finite-size corrections in replica symmetry breaking.

[1] Phys. Rev. Lett. 86(2001)5211, DOI: 10.1103/PhysRevLett.86.5211
[2] Eur. Phys. J. B 46(2005)501, DOI: 10.1140/epjb/e2005-00280-6
[3] https://arxiv.org/abs/1906.10036
[4] "Ground State Properties of the Diluted Sherrington-Kirkpatrick Spin Glass", (in preparation), see https://arxiv.org/search/?query=boettcher_s_1&searchtype=all&source=header