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Phys Rev Lett. 2012 Jun 22;108(25):255703. Epub 2012 Jun 21.

Generalized scaling theory for critical phenomena including essential singularities and infinite dimensionality.

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Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.


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.

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