Anomalous criticality coexists with giant cluster in the uniform forest model Articles uri icon

publication date

  • May 2024

start page

  • 1

end page

  • 11

issue

  • 5

volume

  • 16, 121

International Standard Serial Number (ISSN)

  • 2542-4653

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.

subjects

  • Mathematics