Generalized scaling theory for critical phenomena including essential   singularity and infinite dimensionality
  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. 
Tomoaki Nogawa, Takehisa Hasegawa and Koji Nemoto
cond-mat.stat-mech cond-mat.dis-nn