Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2005-01-22
Physical Review B 71, 214409 (2005).
Physics
Condensed Matter
Statistical Mechanics
corrected version, 10 pages, RevTex4, 12 ps-figures included; related papers available a http://www.physics.emory.edu/faculty/
Scientific paper
10.1103/PhysRevB.71.214409
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, $d_c=6$. 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 $d=3$ with Gaussian bonds.
Boettcher Stefan
Cooke S. E.
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