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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/10054/9069

Title: Critical behavior of loops and biconnected clusters on fractals of dimension d < 2
Authors: DAS, D
DEY, S
JACOBSEN, JL
DHAR, D
Keywords: self-avoiding walks
honeycomb lattice
o(n) model
sierpinski gasket
exact exponents
transfer-matrix
percolation
transition
backbone
Issue Date: 2008
Publisher: IOP PUBLISHING LTD
Citation: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 41(48), -
Abstract: We solve the O(n) model, defined in terms of self- and mutually avoiding loops coexisting with voids, on a 3-simplex fractal lattice, using an exact real space renormalization group technique. As the density of voids is decreased, the model shows a critical point, and for even lower densities of voids, there is a dense phase showing power-law correlations, with critical exponents that depend on n, but are independent of density. At n = -2 on the dilute branch, a trivalent vertex defect acts as a marginal perturbation. We define a model of biconnected clusters which allows for a finite density of such vertices. As n is varied, we get a line of critical points of this generalized model, emanating from the point of marginality in the original loop model. We also study another perturbation of adding local bending rigidity to the loop model, and find that it does not affect the universality class.
URI: http://dx.doi.org/10.1088/1751-8113/41/48/485001
http://dspace.library.iitb.ac.in/xmlui/handle/10054/9069
http://hdl.handle.net/10054/9069
ISSN: 1751-8113
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