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

@article{Beaton2014TheCF, title={The Critical Fugacity for Surface Adsorption of Self-Avoiding Walks on the Honeycomb Lattice is \$\$\{1+\sqrt\{2\}\}\$\$1+2}, author={Nicholas R. Beaton and Mireille Bousquet-M{\'e}lou and Jan de Gier and Hugo Duminil-Copin and Anthony J. Guttmann}, journal={Communications in Mathematical Physics}, year={2014}, volume={326}, pages={727-754} }

In 2010, Duminil-Copin and Smirnov proved a long-standing conjecture of Nienhuis, made in 1982, that the growth constant of self-avoiding walks on the hexagonal (a.k.a. honeycomb) lattice is $${\mu=\sqrt{2+\sqrt{2}}}$$μ=2+2. A key identity used in that proof was later generalised by Smirnov so as to apply to a general O(n) loop model with $${n\in [-2,2]}$$n∈[-2,2] (the case n = 0 corresponding to self-avoiding walks). We modify this model by restricting to a half-plane and introducing a surface… CONTINUE READING

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SHOWING 1-10 OF 24 REFERENCES

## Discrete Complex Analysis and Probability

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Exact Critical Point and Critical Exponents of O ( n ) Models in Two Dimensions

VIEW 7 EXCERPTS

HIGHLY INFLUENTIAL

## Self-avoiding Walks and Polymer Adsorption: Low Temperature Behaviour

VIEW 6 EXCERPTS

HIGHLY INFLUENTIAL

## Self-avoiding walks interacting with a surface

VIEW 6 EXCERPTS

HIGHLY INFLUENTIAL

## Self‐avoiding walks terminally attached to an interface

VIEW 6 EXCERPTS

HIGHLY INFLUENTIAL

## Self-Avoiding Walk is Sub-Ballistic

VIEW 2 EXCERPTS