Reduction of spin glasses applied to the Migdal-Kadanoff hierarchical lattice

S. Boettcher

The European Physical Journal B: Condensed Matter and Complex Systems, 2003, vol. 33, issue 4, 439-445

Abstract: A reduction procedure to obtain ground states of spin glasses on sparse graphs is developed and tested on the hierarchical lattice associated with the Migdal-Kadanoff approximation for low-dimensional lattices. While more generally applicable, these rules here lead to a complete reduction of the lattice. The stiffness exponent governing the scaling of the defect energy ΔE with system size L, σ(ΔE) ~L y , is obtained as y 3 =0.25546(3) by reducing the equivalent of lattices up to L=2 100 in d=3, and as y 4 =0.76382(4) for up to L=2 35 in d=4. The reduction rules allow the exact determination of the ground state energy, entropy, and also provide an approximation to the overlap distribution. With these methods, some well-know and some new features of diluted hierarchical lattices are calculated. Copyright EDP Sciences, Springer-Verlag 2003

Keywords: 05.50.+q Lattice theory and statistics (Ising; Potts; etc.); 75.10.Nr Spin-glass and other random models; 02.60.Pn Numerical optimization (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1140/epjb/e2003-00184-5

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