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

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