On the Convergence of the Expansion of Renormalization Group Flow Equation

TL;DR

This paper analyzes the convergence and reliability of polynomial truncation methods in solving the exact renormalization group flow equations for fermionic models, comparing them with grid solutions and examining cutoff sensitivities.

Contribution

It provides a comparative study of polynomial truncation versus grid solutions for RG equations, assessing their validity across different phase transition types.

Findings

Polynomial truncation results depend on cutoff functions.

Expansion method is valid for second-order phase transitions.

Grid solutions offer more accurate results for first-order transitions.

Abstract

We compare and discuss the dependence of a polynomial truncation of the effective potential used to solve exact renormalization group flow equation for a model with fermionic interaction (linear sigma model) with a grid solution. The sensitivity of the results on the underlying cutoff function is discussed. We explore the validity of the expansion method for second and first-order phase transitions.