Hybrid cluster+RG approach to the theory of phase transitions in strongly coupled Landau-Ginzburg-Wilson model

TL;DR

This paper introduces a hybrid approach combining cluster methods and renormalization-group techniques to analyze phase transitions in strongly coupled Landau-Ginzburg-Wilson models, improving accuracy across scales.

Contribution

It develops a generalized layer-cake RG scheme integrated with cluster methods for better analysis of strongly coupled field-theoretic models.

Findings

Accurate calculation of magnetization curve and critical temperature.

Good agreement with Monte Carlo simulations.

Effective handling of large scale fluctuations.

Abstract

It is argued that cluster methods provide a viable alternative to Wilson's momentum shell integration technique at the early stage of renormalization in the field-theoretic models with strongly coupled fields because these methods allow for systematic accounting of all interactions in the system irrespective of their strength. These methods, however, are restricted to relatively small spatial scales, so they ought to be supplemented with more conventional renormalization-group (RG) techniques to account for large scale correlations. To fulfil this goal a "layer-cake" renormalization scheme earlier developed for rotationally symmetric Hamiltonians has been generalized to the lattice case. The RG technique can be naturally integrated with an appropriately modified cluster method so that the RG equations were used only in the presence of large scale fluctuations, while in their absence the approach reduced to a conventional cluster method. As an illustrative example the simplest single-site cluster approximation together with the local-potential RG equation are applied to simple cubic Ising model to calculate several non-universal quantities such as the magnetization curve, the critical temperature, and some critical amplitudes. Good agreement with Monte Carlo simulations and series expansion results was found.