Polymerization on the diamond hierarchical lattice: The Migdal-Kadanoff renormalization-group scheme

Polymerization on the diamond hierarchical lattice: The Migdal-Kadanoff renormalization-group scheme.

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

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 ∆E with system size L, σ(...

The ±J spin glass in Migdal-Kadanoff approximation

We study the low-temperature phase of the three-dimensional ±J Ising spin glass in MigdalKadanoff approximation. At zero temperature, T = 0, the properties of the spin glass result from the ground-state degeneracy and can be elucidated using scaling arguments based on entropy. The approach to the asymptotic scaling regime is very slow, and the correct exponents are only visible beyond system si...

The Hierarchical Model and the Renormalization Group

The models tha t we consider are 1-dimensionM ferromagnets with a ra ther peculiar, nontranslat ionMly invar iant interact ion [1-4]. I t will be seen tha t the special form of this interact ion leads to a ra ther simple formulat ion of the renormalizat ion group equation. Apar t f rom the lack of t ranslat ion invariance these models are supposed to behave in m a n y respects like ordinary 1-d...

On the Renormalization Group Transformation for Scalar Hierarchical Models

We give a new proof for the existence of a non{Gaussian hierarchical renormalization group xed point, using what could be called a beta{function for this problem. We also discuss the asymptotic behavior of this xed point, and the connection between the hierarchical models of Dyson and Gallavotti. 1 Supported in Part by the National Science Foundation under Grant No. DMS{8802590. 2 Supported in ...