Ultrametricity in the infinite ranged Ising spin glass.

Monte Carlo simulations have been used to study the development of ultrametricity in the low temperature phase of the infinite ranged Sherrington-Kirpatrick model of the Ising spin glass. Equilibrium configuration overlap data have been obtained for sizes (N) between N = 16 and 512 spins at the transition temperature T = T(c) and in the spin glass phase at T = 0.6T(c). The latter show clear evidence for the emergence in the thermodynamic limit of isosceles triangles among the triangles formed by the three mutual overlaps of three configurations, as predicted by Mezard et al.