Low-temperature phase boundary of dilute-lattice spin glasses

The thermal-to-percolative crossover exponent ϕ, well known for ferromagnetic systems, is studied extensively for Edwards–Anderson spin glasses. The scaling of defect energies are determined at the bond percolation threshold p_c using an improved reduction algorithm. Simulations extend to system sizes above N=10⁸ in dimensions d=2,…,7. The results can be related to the behavior of the transition temperature T_g∼(p−p_c)^ϕ between the paramagnetic and the glassy regime for p↘p_c. In three dimensions, where our simulations predict ϕ=1.127(5), this scaling form for T_g provides a rare experimental test of predictions arising from the equilibrium theory of low-temperature spin glasses. For dimensions near and above the upper critical dimension, the results provide a challenge to reconcile mean-field theory with finite-dimensional properties.