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 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 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)^ϕbetween 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 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/
References in corpus (5)
- Stiffness of the Edwards-Anderson Model in all Dimensions
- Percolation on two- and three-dimensional lattices
- Stiffness Exponents for Lattice Spin Glasses in Dimensions d=3,...,6
- Low-Temperature Excitations of Dilute Lattice Spin Glasses
- Reduction of Spin Glasses applied to the Migdal-Kadanoff Hierarchical Lattice