Critical behavior of the site percolation model on the square lattice in a L×M geometry

Relevant aspects of the critical behavior of the site percolation model in a L×M geometry (L≪M) are studied. It is shown that this geometry favors the growth of percolating clusters in the L-direction with respect to those growing in the M-direction, causing pronounced finite-size effects on the per...

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Autores principales: Monetti, Roberto Adrián, Albano, Ezequiel Vicente
Formato: Articulo
Lenguaje:Inglés
Publicado: 1991
Materias:
Física
Spectroscopy
Neural Network
Complex System
Monte Carlo Simulation
Asymptotic Behavior
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/146376
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-146376
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Física
Spectroscopy
Neural Network
Complex System
Monte Carlo Simulation
Asymptotic Behavior
spellingShingle Física
Spectroscopy
Neural Network
Complex System
Monte Carlo Simulation
Asymptotic Behavior
Monetti, Roberto Adrián
Albano, Ezequiel Vicente
Critical behavior of the site percolation model on the square lattice in a L×M geometry
topic_facet Física
Spectroscopy
Neural Network
Complex System
Monte Carlo Simulation
Asymptotic Behavior
description Relevant aspects of the critical behavior of the site percolation model in a L×M geometry (L≪M) are studied. It is shown that this geometry favors the growth of percolating clusters in the L-direction with respect to those growing in the M-direction, causing pronounced finite-size effects on the percolation probabilities. Scaling functions have an additional parameter, namely M, which introduces a dependence of these functions on the aspect ratio L/M. At criticality, the probability of a site belonging to the percolation clusters (PL,M) behaves like PL,M∝Lβ/vφ(L/M) with β=5/36 and v=4/3, where φ is a suitable scaling function. Using scaling arguments it is conjectured and then tested by means of Monte Carlo simulations, the following asymptotic behavior φ(L/M)∝(L/M)δ, (L→∞,M→∞, δ=1), for the leading term. Systematic deviations of the Monte Carlo data from the conjectured behavior are due to second order corrections to the leading term which can also be under-stood on the basis of scaling ideas. Finite-size dependent “critical probabilities” are also functions of L/M as it follows from scaling arguments which are corroborated by the simulations.
format Articulo
Articulo
author Monetti, Roberto Adrián
Albano, Ezequiel Vicente
author_facet Monetti, Roberto Adrián
Albano, Ezequiel Vicente
author_sort Monetti, Roberto Adrián
title Critical behavior of the site percolation model on the square lattice in a L×M geometry
title_short Critical behavior of the site percolation model on the square lattice in a L×M geometry
title_full Critical behavior of the site percolation model on the square lattice in a L×M geometry
title_fullStr Critical behavior of the site percolation model on the square lattice in a L×M geometry
title_full_unstemmed Critical behavior of the site percolation model on the square lattice in a L×M geometry
title_sort critical behavior of the site percolation model on the square lattice in a l×m geometry
publishDate 1991
url http://sedici.unlp.edu.ar/handle/10915/146376
work_keys_str_mv AT monettirobertoadrian criticalbehaviorofthesitepercolationmodelonthesquarelatticeinalmgeometry
AT albanoezequielvicente criticalbehaviorofthesitepercolationmodelonthesquarelatticeinalmgeometry
bdutipo_str Repositorios
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