Anomalous criticality coexists with giant cluster in the uniform forest model

TL;DR

This paper reveals that in the supercritical phase of the 3D uniform forest model, an infinite tree coexists with critical phenomena and exhibits anomalous scaling behaviors, challenging traditional understandings of phase transitions.

Contribution

The study uncovers the simultaneous presence of critical phenomena and giant clusters in the supercritical phase of the uniform forest model, highlighting novel anomalous scaling behaviors.

Findings

Presence of an infinite tree in the supercritical phase.

Emergence of anomalous scaling behaviors and multiple fractal dimensions.

Giant-tree size fluctuations do not follow the central-limit theorem.

Abstract

We show by extensive simulations that the whole supercritical phase of the three-dimensional uniform forest model simultaneously exhibits an infinite tree and a rich variety of critical phenomena. Besides typical scalings like algebraically decaying correlation, power-law distribution of cluster sizes, and divergent correlation length, a number of anomalous behaviors emerge. The fractal dimensions for off-giant trees take different values when being measured by linear system size or gyration radius. The giant-tree size displays two-length scaling fluctuations, instead of following the central-limit theorem.