Generalized scaling theory for critical phenomena including essential singularity 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.

5 pages, 3 figures

References in corpus (4)

• Critical phenomena in complex networks
• Ordinary Percolation with Discontinuous Transitions
• Small-World Bonds and Patchy Percolation on the Hanoi Network
• Generating-function approach for bond percolations in hierarchical networks

Cited by in corpus (10)

• Transition-type change between an inverted Berezinskii-Kosterlitz-Thouless transition and an abrupt transition in the bond percolation on a random hierarchical small-world network
• Scaling of Clusters near Discontinuous Percolation Transitions in Hyperbolic Networks
• Classification of critical phenomena in hierarchical small-world networks
• Criticality governed by the stable renormalization fixed point of the Ising model in the hierarchical small-world network
• From explosive to infinite-order transitions on a hyperbolic network
• Real-Space Renormalization Group for Spectral Properties of Hierarchical Networks
• Absence of the non-percolating phase for percolation on the non-planar Hanoi network
• Renormalization-group theory of the abnormal singularities at the critical-order transition in bond percolation on pointed hierarchical graphs
• Gliding down the QCD transition line, from $N_f=2$ till the onset of conformality
• Renormalization Group Solution of the Chutes&Ladder Model