Deformation of a renormalization-group equation applied to infinite-order phase transitions

TL;DR

This paper introduces a method to analyze the asymptotic behavior of running coupling constants in systems with infinite-order phase transitions by modifying renormalization-group equations, demonstrated through multiple examples.

Contribution

It presents a novel algebraic approach to studying infinite-order phase transitions by adding a linear term to the renormalization-group equation.

Findings

Derived asymptotic behavior of coupling constants

Explicit examples demonstrating the method

Enhanced understanding of infinite-order phase transitions

Abstract

By adding a linear term to a renormalization-group equation in a system exhibiting infinite-order phase transitions, asymptotic behavior of running coupling constants is derived in an algebraic manner. A benefit of this method is presented explicitly using several examples.