Author： Beaton Nicholas R Guttmann Anthony J Jensen Iwan Lawler Gregory F
Publisher： IOP Publishing
E-ISSN： 1751-8121|48|45|454001-454027
ISSN： 1751-8121
Source： Journal of Physics A: Mathematical and Theoretical, Vol.48, Iss.45, 2015-11, pp. : 454001-454027
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Abstract
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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