Generalized Migdal-Kadanoff Bond-moving Renormalization Recursion Procedure I: Symmetrical Half-length Bond Operation on Translational Invariant Lattices

TL;DR

This paper introduces a symmetrical half-length bond operation in a generalized Migdal-Kadanoff renormalization group method, applied to Gaussian models on triangular lattices, yielding results consistent with classical critical exponent findings.

Contribution

It presents a novel symmetrical bond operation within the Migdal-Kadanoff framework for translational invariant lattices, enhancing the method's applicability.

Findings

Correlation length critical exponents match classical results

Demonstrates the effectiveness of the symmetrical bond operation

Applicable to Gaussian models on triangular lattices

Abstract

We report in a series of papers two types of generalized Migdal-Kadanoff bond-moving renormalization group transformation recursion procedures. In this first part the symmetrical operation of half length bonds on translational invariant lattices are considered. As an illustration of their predominance in application, the procedures are used to study the critical behavior of the spin-continuous Gaussian model constructed on the triangular lattices. Results such as the correlation length critical exponents obtained by this means are found to be in good conformity with the classical results from other studies.