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

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  • S. Boettcher

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

Suggested Citation

  • S. Boettcher, 2003. "Reduction of spin glasses applied to the Migdal-Kadanoff hierarchical lattice," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 33(4), pages 439-445, June.
    • Handle: RePEc:spr:eurphb:v:33:y:2003:i:4:p:439-445
    DOI: 10.1140/epjb/e2003-00184-5
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