Adsorbing Motzkin paths

Rensburg, E J Janse van

doi:10.1088/1751-8113/43/48/485006

Cited by 4 publications

(3 citation statements)

References 42 publications

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“…We note here that all the existing models discussed in section 1.1 have second-order adsorption transitions [12,14,26]. Moreover, the general SAW model in two dimensions is also conjectured [15] to exhibit a second-order transition.…”

Section: Order Of the Phase Transitionmentioning

confidence: 59%

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

Beaton¹,

Iliev²

2015

J. Stat. Mech.

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Prudent walks are self-avoiding walks which cannot step towards an already occupied vertex. We introduce a new model of adsorbing prudent walks on the square lattice, which start on an impenetrable surface and accrue a fugacity a with each step along the surface. These are different to other exactly solved models of polymer adsorption, like Dyck paths, Motzkin paths and partially-directed walks, in that they are not trivially directed -they are able to step in all lattice directions. We calculate the generating functions, free energies and surface densities for this model and observe a first-order adsorption transition at the critical value of the surface interaction.

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Section: Order Of the Phase Transitionmentioning

confidence: 59%

“…• Motzkin paths. [14] These are generated on the triangular lattice by forbidding NW, W and SW steps. The growth constant is µ = 3, and the phase transition occurs at = a 2 c for edge weights and = a 3/2 c for vertex weights.…”

Section: Exactly Solved Modelsmentioning

confidence: 99%

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

Beaton¹,

Iliev²

2015

J. Stat. Mech.

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“…Note that = y e f kT . Motzkin paths with raised end-points have been investigated in [74]. For a walk of length n the two end-points are fixed at heights ⌊ ⌋ an and ⌊ ⌋ bn above the distinguished line.…”

Section: Motzkin Paths Motzkin Pathsmentioning

confidence: 99%

Statistical mechanics of polymers subject to a force

Orlandini¹,

Whittington²

2016

J. Phys. A: Math. Theor.

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When a polymer molecule is subjected to a force (such as a tensile force) it responds and this response gives information about the thermodynamics and structural properties of the polymer. In recent years there have been a number of experimental developments, such as atomic force microscopy and optical tweezers, that allow individual polymer molecules to be pulled in various ways. This has resulted in a renewed theoretical interest in how polymers respond to applied forces. This review will focus on some particular aspects of this field. We shall be primarily interested in tensile forces and consider various scenarios, such as pulling an adsorbed polymer from a surface and pulling a polymer from one phase to another. In order to make theoretical progress one needs a model of the polymer and we shall focus on lattice models. Our emphasis will be on exactly solvable models such as Dyck and Motzkin paths, and on rigorous results for self-avoiding walk models and some relatives, though we shall also discuss scaling theories and some selected numerical results.

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Motzkin numbers out of Random Domino Automaton

Białecki¹

2012

Physics Letters A

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Adsorbing Motzkin paths

Cited by 4 publications

References 42 publications

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

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

Statistical mechanics of polymers subject to a force

Motzkin numbers out of Random Domino Automaton

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