TY - JOUR
T1 - Floppy modes and the free energy
T2 - Rigidity and connectivity percolation on Bethe lattices
AU - Duxbury, P. M.
AU - Jacobs, D. J.
AU - Thorpe, M. F.
AU - Moukarzel, C.
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 1999
Y1 - 1999
N2 - We show that the negative of the number of floppy modes behaves as a free energy for both connectivity and rigidity percolation, and we illustrate this result using Bethe lattices. The rigidity transition on Bethe lattices is found to be first order at a bond concentration close to that predicted by Maxwell constraint counting. We calculate the probability of a bond being on the infinite cluster and also on the overconstrained part of the infinite cluster, and show how a specific heatcan be defined as the second derivative of the free energy. We demonstrate that the Bethe lattice solution is equivalent to that of the random bond model, where points are joined randomly (with equal probability at all length scales) to have a given coordination, and then subsequently bonds are randomly removed.
AB - We show that the negative of the number of floppy modes behaves as a free energy for both connectivity and rigidity percolation, and we illustrate this result using Bethe lattices. The rigidity transition on Bethe lattices is found to be first order at a bond concentration close to that predicted by Maxwell constraint counting. We calculate the probability of a bond being on the infinite cluster and also on the overconstrained part of the infinite cluster, and show how a specific heatcan be defined as the second derivative of the free energy. We demonstrate that the Bethe lattice solution is equivalent to that of the random bond model, where points are joined randomly (with equal probability at all length scales) to have a given coordination, and then subsequently bonds are randomly removed.
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U2 - 10.1103/PhysRevE.59.2084
DO - 10.1103/PhysRevE.59.2084
M3 - Article
AN - SCOPUS:0000794168
VL - 59
SP - 2084
EP - 2092
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
SN - 1539-3755
IS - 2
ER -