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

Tomoaki Nogawa, Takehisa Hasegawa, Koji Nemoto

Published 2012-06-22, updated 2014-02-28Version 2

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.