title: Generalized scaling theory for critical phenomena including essential singularities and infinite dimensionality.
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.
authors.affiliation: Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan. nogawa@serow.t.u-tokyo.ac.jp
authors.forename: Tomoaki
authors.initials: T
authors.lastname: Nogawa
authors.forename: Takehisa
authors.initials: T
authors.lastname: Hasegawa
authors.forename: Koji
authors.initials: K
authors.lastname: Nemoto