Compressed self-avoiding walks, bridges and polygons
Nicholas R Beaton, Anthony J Guttmann, Iwan Jensen, Gregory F Lawler
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | IOP PUBLISHING LTD | Published : 2015
We study various self-avoiding walks (SAWs) which are constrained to lie in the upper half-plane and are subjected to a compressive force. This force is applied to the vertex or vertices of the walk located at the maximum distance above the boundary of the half-space. In the case of bridges, this is the unique end-point. In the case of SAWs or self-avoiding polygons, this corresponds to all vertices of maximal height. We first use the conjectured relation with the Schramm-Loewner evolution to predict the form of the partition function including the values of the exponents, and then we use series analysis to test these predictions.
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Awarded by Australian Research Council
Awarded by National Science Foundation
This work was supported by an award (IJ) under the Merit Allocation Scheme on the NCI National Facility at the ANU and by funding under the Australian Research Council's Discovery Projects scheme by the grant DP140101110 (AJG and IJ). Gregory Lawler is supported by National Science Foundation grant DMS-0907143. Nicholas Beaton is supported by the Pacific Institute for the Mathematical Sciences.