Low-Temperature Phase Boundary of dilute Lattice Spin Glasses
arXiv:0710.0041 · doi:10.1016/j.physa.2007.07.016
Abstract
The thermal-to-percolative crossover exponent Ï, 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 algorithm. Simulations extend to system sizes above N=10^8 in dimensions d=2,...,7. The results can be related to the behavior of the transition temperature T_g (p-p_c)^Ïbetween the paramagnetic and the glassy regime for p-> p_c. In three dimensions, where our simulations predict Ï=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 dimension near and above the upper critical dimension, the results provide a new challenge to reconcile mean-field theory with finite-dimensional properties.
4 pages, added figure and other improvements, final version, related information can be found at http://www.physics.emory.edu/faculty/boettcher/