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Dive into the research topics where Nicholas R. Beaton is active.

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Featured researches published by Nicholas R. Beaton.


Journal of Physics A | 2012

Two-dimensional self-avoiding walks and polymer adsorption: critical fugacity estimates

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

Compressed self-avoiding walks, bridges and polygons*

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

A numerical adaptation of self-avoiding walk identities from the honeycomb to other 2D lattices

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

The critical pulling force for self-avoiding walks

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

Some New Self-avoiding Walk and Polygon Models

Nicholas R. Beaton; Philippe Flajolet; Timothy M. Garoni; A J Guttmann

y = e^f


Journal of Physics A | 2010

The unusual asymptotics of three-sided prudent polygons

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

Two-sided prudent walks: a solvable non-directed model of polymer adsorption

Nicholas R. Beaton; Gerasim K. Iliev

y_c


Journal of Physics A | 2014

The critical surface fugacity of self-avoiding walks on a rotated honeycomb lattice

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

The Critical Fugacity for Surface Adsorption of Self-Avoiding Walks on the Honeycomb Lattice is {1+\sqrt{2}}

Nicholas R. Beaton; Mireille Bousquet-Mélou; Jan de Gier; Hugo Duminil-Copin; A J Guttmann

y_c=1


Journal of Combinatorial Theory | 2011

The enumeration of prudent polygons by area and its unusual asymptotics

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.

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A J Guttmann

University of Melbourne

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Iwan Jensen

University of Melbourne

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Jan de Gier

University of Melbourne

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Jeremy W. Eng

University of Saskatchewan

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A R Conway

University of Melbourne

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