# 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.

## Key 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.

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Source: https://tomesphere.com/paper/hep-lat/9602014