Generalized scaling theory for critical phenomena including essential singularity and infinite dimensionality

TL;DR

This paper introduces a comprehensive scaling theory for critical phenomena that encompasses both power-law and essential singularities across finite and infinite dimensional systems, validated through analysis of the Potts model.

Contribution

It presents a unified scaling framework that accounts for essential singularities and infinite dimensionality, supported by analysis of a hierarchical network model.

Findings

Validates the scaling theory using the Potts model

Identifies saddle-node bifurcation as key to essential singularity

Extends critical phenomena understanding to infinite dimensions

Abstract

We propose a generic scaling theory for critical phenomena that includes power-law and essential singularities in finite and infinite dimensional systems. In addition, we clarify its validity by analyzing the Potts model in a simple hierarchical network, where a saddle-node bifurcation of the renormalization-group fixed point governs the essential singularity.