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Obtaining Stiffness Exponents from Bond-diluted Lattice Spin Glasses

S. Boettcher·S. E. Cooke
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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, $d_c=6$. 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.

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BibTeXRIS

S. Boettcher, S. E. Cooke. 2005-03-24. Obtaining Stiffness Exponents from Bond-diluted Lattice Spin Glasses. https://doi.org/10.1103/physrevb.71.214409

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