Beta Function Constraints from Renormalization Groups Flows in Spin Systems

TL;DR

This paper explores a new consistency condition linking beta functions and renormalization group flows in spin systems, providing a tool to evaluate the accuracy of approximate RG flows and suggest improved equations.

Contribution

It introduces a novel consistency condition between beta functions and RG flows, applicable to both exact and approximate cases in spin models.

Findings

The condition holds for models with exact RG flows.

The condition is violated by approximate RG flows.

Deviation from the condition can test RG flow quality.

Abstract

Inspired by previous work on the constraints that duality imposes on beta functions of spin models, we propose a consistency condition between those functions and RG flows at different points in coupling constant space. We show that this consistency holds for a non self-dual model which admits an exact RG flow, but that it is violated when the RG flow is only approximate. We discuss the use of this deviation as a test for the ``goodness'' of proposed RG flows in complicated models, and the use of the proposed consistency in suggesting RG equations.