Conformal invariance in three dimensional percolation
Year: 2015
Authors: Gori G., Trombettoni A.
Autors Affiliation: CNR IOM DEMOCRITOS Simulat Ctr, I-34136 Trieste, Italy; SISSA, I-34136 Trieste, Italy; Ist Nazl Fis Nucl, I-34127 Trieste, Italy.
Abstract: The aim of the paper is to present numerical results supporting the presence of conformal invariance in three dimensional statistical mechanics models at criticality and to elucidate the geometric aspects of universality. As a case study we study three dimensional percolation at criticality in bounded domains. Both on discrete and continuous models of critical percolation, we test by numerical experiments the invariance of quantities in finite domains under conformal transformations focusing on crossing probabilities. Our results show clear evidence of the onset of conformal invariance in finite realizations especially for the continuum percolation models. Finally we propose a simple analytical function approximating the crossing probability among two spherical caps on the surface of a sphere and confront it with the numerical results.
Journal/Review: JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
KeyWords: conformal field theory (theory); classical phase transitions (theory); surface effects (theory); percolation problems (theory)DOI: 10.1088/1742-5468/2015/07/P07014Citations: 12data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2025-09-14References taken from IsiWeb of Knowledge: (subscribers only)
