Self-consistent Calculation of Real Space Renormalization Group Flows and Effective Potentials

TL;DR

This paper introduces a self-consistent method for calculating real space renormalization group flows in lattice scalar field theories, using saddle point integration and preserving a simple action parameterization without polynomial field approximations.

Contribution

It presents a novel self-consistent approach to compute RG flows that maintains a simple action form and avoids polynomial approximations, enhancing accuracy in lattice field theory.

Findings

Effective computation of RG flows in scalar field theories.

Preservation of simple action parameterization during flow.

No polynomial approximation in field variables.

Abstract

We show how to compute real space renormalization group flows in lattice field theory by a self-consistent method. In each step, the integration over the fluctuation field (high frequency components of the field) is performed by a saddle point method. The saddle point depends on the block-spin. Higher powers of derivatives of the field are neglected in the actions, but no polynomial approximation in the field is made. The flow preserves a simple parameterization of the action. In this paper we treat scalar field theories as an example.