Asymptotics of polygons in restricted geometries subject to a force

Nicholas R. Beaton (1) , Jeremy Eng (1) , Christine Soteros (1)

1 Department of Mathematics and Statistics, [Regina, Saskatchewan]

We consider self-avoiding polygons in a restricted geometry, namely an infinite L × M tube in Z3. These polygons are subjected to a force f, parallel to the infinite axis of the tube. When f > 0 the force stretches the polygons, while when f < 0 the force is compressive. In this extended abstract we obtain and prove the asymptotic form of the free energy in the limit f → −∞. We conjecture that the f → −∞ asymptote is the same as the free energy of Hamiltonian polygons, which visit every vertex in a L × M × N box.

Domaines: Combinatoire [math.CO]

Nicholas R. Beaton, Jeremy Eng, Christine Soteros. Asymptotics of polygons in restricted geometries subject to a force. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6330⟩. ⟨hal-02173749⟩