Reduction of spin glasses applied to the Migdal-Kadanoff hierarchical lattice
Physics Department, Emory University, Atlanta, Georgia
Revised: 4 April 2003
Published online: 3 July 2003
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 with system size L, , is obtained as by reducing the equivalent of lattices up to in d=3, and as for up to 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.
PACS: 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 75.10.Nr – Spin-glass and other random models / 02.60.Pn – Numerical optimization
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2003