Obtaining Stiffness Exponents from Bond-diluted Lattice Spin Glasses
Abstract
Recently, a method has been proposed to obtain accurate predictions for low-temperature properties of lattice spin glasses that is practical even above the upper critical dimension, . This method is based on the observation that bond-dilution enables the numerical treatment of larger lattices, and that the subsequent combination of such data at various bond densities into a finite-size scaling Ansatz produces more robust scaling behavior. In the present study we test the potential of such a procedure, in particular, to obtain the stiffness exponent for the hierarchical Migdal-Kadanoff lattice. Critical exponents for this model are known with great accuracy and any simulations can be executed to very large lattice sizes at almost any bond density, effecting a insightful comparison that highlights the advantages -- as well as the weaknesses -- of this method. These insights are applied to the Edwards-Anderson model in with Gaussian bonds.
Cite
@article{arxiv.cond-mat/0501547,
title = {Obtaining Stiffness Exponents from Bond-diluted Lattice Spin Glasses},
author = {S. Boettcher and S. E. Cooke},
journal= {arXiv preprint arXiv:cond-mat/0501547},
year = {2009}
}
Comments
corrected version, 10 pages, RevTex4, 12 ps-figures included; related papers available a http://www.physics.emory.edu/faculty/boettcher/