Nicholas R. Beaton
University of Melbourne
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Featured researches published by Nicholas R. Beaton.
Journal of Physics A | 2012
Nicholas R. Beaton; A J Guttmann; Iwan Jensen
Recently Beaton, de Gier and Guttmann proved a conjecture of Batchelor and Yung that the critical fugacity of self-avoiding walks (SAW) interacting with (alternate)sitesonthesurfaceofthehoneycomblatticeis1+ √ 2.Akeyidentity used in that proof depends on the existence of a parafermionic observable for SAW interacting with a surface on the honeycomb lattice. Despite the absence ofacorrespondingobservableforSAWonthesquareandtriangularlattices,we show that in the limit of large lattices, some of the consequences observed for the honeycomb lattice persist irrespective of lattice. This permits the accurate estimation of the critical fugacity for the corresponding problem for the square and triangular lattices. We consider both edge and site weighting, and results of unprecedented precision are achieved. We also prove the corresponding result for the edge-weighted case for the honeycomb lattice.
Journal of Physics A | 2015
Nicholas R. Beaton; A J Guttmann; Iwan Jensen; Gregory F. Lawler
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.
Journal of Physics A | 2012
Nicholas R. Beaton; A J Guttmann; Iwan Jensen
Recently, Duminil-Copin and Smirnov proved a long-standing conjecture of Nienhuis that the connective constant of self-avoiding walks (SAWs) on the honeycomb lattice is
Journal of Physics A | 2015
Nicholas R. Beaton
Self-avoiding walks are a simple and well-known model of long, flexible polymers in a good solvent. Polymers being pulled away from a surface by an external agent can be modelled with self-avoiding walks in a half-space, with a Boltzmann weight
Fundamenta Informaticae | 2012
Nicholas R. Beaton; Philippe Flajolet; Timothy M. Garoni; A J Guttmann
y = e^f
Journal of Physics A | 2010
Nicholas R. Beaton; Philippe Flajolet; A J Guttmann
associated with the pulling force. This model is known to have a critical point at a certain value
Journal of Statistical Mechanics: Theory and Experiment | 2015
Nicholas R. Beaton; Gerasim K. Iliev
y_c
Journal of Physics A | 2014
Nicholas R. Beaton
of this Boltzmann weight, which is the location of a transition between the so-called free and ballistic phases. The value
Communications in Mathematical Physics | 2014
Nicholas R. Beaton; Mireille Bousquet-Mélou; Jan de Gier; Hugo Duminil-Copin; A J Guttmann
y_c=1
Journal of Combinatorial Theory | 2011
Nicholas R. Beaton; Philippe Flajolet; A J Guttmann
has been conjectured by several authors using numerical estimates. We provide a relatively simple proof of this result, and show that further properties of the free energy of this system can be determined by re-interpreting existing results about the two-point function of self-avoiding walks.