Anomalous criticality coexists with giant cluster in the uniform forest model

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.

11 pages, 3 figures. Pdflatex. SciPost Physics style SciPost.cls is included. Minor differences with respect to v2. Final version

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