Acta Physica Sinica

SELF-CONSISTENT CORRELATED PERCOLATION

Zhao-Qing Zhang, 中国科学院物理研究所

Published Jan 1, 1982• 0 citations

Abstract

The critical properties of a quenched site-correlated percolation system is treated by real-space renormalization group method. We chose the nearest-neighbour short-range order a as the correlation parameter. By treating the correlated probability self-consistently, we found, in two dimension, there is only one nontrivial physical fixed point and the correlation is an irrelevant parameter at random percolation fixed point, which is consistent with other correlated percolation models.

DOI: 10.7498/aps.31.1576

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Acta Physica Sinica

SELF-CONSISTENT CORRELATED PERCOLATION

Zhao-Qing Zhang, 中国科学院物理研究所

Published Jan 1, 1982• 0 citations

Publisher

Abstract

DOI: 10.7498/aps.31.1576

Related papers

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Tiecheng Li, 中国科学院物理研究所

The percolation problem for the 2-D triangular lattice of the quenched-correlated system is studied by using real-space renormalization group method. The many-body correlations for the occupied sites are considered by Kirkwood's superposition approximation approach and those for occupied and unoccupied sites by a procedure which holds the conservation of probability. The scheme is applied to the case including 3-body correlation and to that with next nearest neighboring correlations. Our conclusion is that, in either case the universality in critical phenomena of percolation ia unchanged, even some complicated correlations are involved.The percolation problem for the 2-D triangular lattice of the quenched-correlated system is studied by using real-space renormalization group method. The many-body correlations for the occupied sites are considered by Kirkwood's superposition approximation approach and those for occupied and unoccupied sites by a procedure which holds the conservation of probability. The scheme is applied to the case including 3-body correlation and to that with next nearest neighboring correlations. Our conclusion is that, in either case the universality in critical phenomena of percolation ia unchanged, even some complicated correlations are involved.

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Physical review. B, Condensed matterJan 1, 1984177 citations

x

.. For

a<d

the correlations are relevant if $a\ensuremath{\nu}\ensuremath{-}2<0$ (where $\ensuremath{\nu}$ is the percolation correlation-length exponent), while for

a>d

the correlations are relevant if $d\ensuremath{\nu}\ensuremath{-}2<0$.. Applying this criterion to the behavior that results when the correlations are relevant, we argue that the new behavior will have ${\ensuremath{\nu}}_{\mathrm{long}}=\frac{2}{a}$.. It is shown that the correlated bond percolation problem is equivalent to a

q

-state Potts model with quenched disorder in the limit $q\ensuremath{\rightarrow}1$.. With the use of this result, a renormalization-group study of the problem is presented, expanding in $\ensuremath{\epsilon}=6\ensuremath{-}d$ and in $\ensuremath{\delta}=4\ensuremath{-}a$.. In addition to the normal percolation fixed point, we find a new long-range fixed point. The crossover to this new fixed point follows the extended Harris criterion, and the fixed point has exponents ${\ensuremath{\nu}}_{\mathrm{long}}=\frac{2}{a}$ (as predicted) and ${\ensuremath{\eta}}_{\mathrm{long}}=\frac{1}{11}(\ensuremath{\delta}\ensuremath{-}\ensuremath{\epsilon})$. Finally, several results on the percolation properties of the Ising model at its critical point are shown to be in agreement with the predictions of this paper.