A general theory is given for the quenched dilute s-state Potts and n-vector models in any dimension d. It is shown that for T→0 at the percolation threshold the Potts thermal exponent νT equals the percolation exponent νp, implying a crossover exponent φ=1, for any s and d. For the n-vector model (n>1), νT=νp/ζR, where ζR is a resistivity critical exponent. Agreement with recent experiments for two-dimensional dilute Ising and Heisenberg systems is excellent.
%0 Journal Article
%1 Coniglio1981Thermal
%A Coniglio, Antonio
%D 1981
%I American Physical Society
%J Physical Review Letters
%K potts-model percolation critical-phenomena
%N 4
%P 250--253
%R 10.1103/physrevlett.46.250
%T Thermal Phase Transition of the Dilute \$s\$-State Potts and \$n\$-Vector Models at the Percolation Threshold
%U http://dx.doi.org/10.1103/physrevlett.46.250
%V 46
%X A general theory is given for the quenched dilute s-state Potts and n-vector models in any dimension d. It is shown that for T→0 at the percolation threshold the Potts thermal exponent νT equals the percolation exponent νp, implying a crossover exponent φ=1, for any s and d. For the n-vector model (n>1), νT=νp/ζR, where ζR is a resistivity critical exponent. Agreement with recent experiments for two-dimensional dilute Ising and Heisenberg systems is excellent.
@article{Coniglio1981Thermal,
abstract = {{A general theory is given for the quenched dilute s-state Potts and n-vector models in any dimension d. It is shown that for T→0 at the percolation threshold the Potts thermal exponent νT equals the percolation exponent νp, implying a crossover exponent φ=1, for any s and d. For the n-vector model (n>1), νT=νp/ζR, where ζR is a resistivity critical exponent. Agreement with recent experiments for two-dimensional dilute Ising and Heisenberg systems is excellent.}},
added-at = {2019-06-10T14:53:09.000+0200},
author = {Coniglio, Antonio},
biburl = {https://www.bibsonomy.org/bibtex/2271e9b3fde809297773bfe1baf18763e/nonancourt},
citeulike-article-id = {9334291},
citeulike-linkout-0 = {http://dx.doi.org/10.1103/physrevlett.46.250},
citeulike-linkout-1 = {http://link.aps.org/abstract/PRL/v46/i4/p250},
citeulike-linkout-2 = {http://link.aps.org/pdf/PRL/v46/i4/p250},
doi = {10.1103/physrevlett.46.250},
interhash = {5867d07fc492d367e83669f5ed9b7ff1},
intrahash = {271e9b3fde809297773bfe1baf18763e},
journal = {Physical Review Letters},
keywords = {potts-model percolation critical-phenomena},
month = jan,
number = 4,
pages = {250--253},
posted-at = {2011-05-23 18:59:18},
priority = {2},
publisher = {American Physical Society},
timestamp = {2019-07-31T12:26:23.000+0200},
title = {{Thermal Phase Transition of the Dilute \$s\$-State Potts and \$n\$-Vector Models at the Percolation Threshold}},
url = {http://dx.doi.org/10.1103/physrevlett.46.250},
volume = 46,
year = 1981
}