344 research outputs found
Pseudo-First-Order Transition in Interacting Self-avoiding Walks and Trails
The coil-globule transition of an isolated polymer has been well established
to be a second-order phase transition described by a standard tricritical O(0)
field theory. We present Monte-Carlo simulations of interacting self-avoiding
walks and interacting self-avoiding trails in four dimensions which provide
compelling evidence that the approach to this (tri)critical point is dominated
by the build-up of first-order-like singularities masking the second-order
nature of the coil-globule transition.Comment: 4 pages with 2 figures included, CCP2001 submissio
Pressure exerted by a vesicle on a surface
Several recent works have considered the pressure exerted on a wall by a
model polymer. We extend this consideration to vesicles attached to a wall, and
hence include osmotic pressure. We do this by considering a two-dimensional
directed model, namely that of area-weighted Dyck paths.
Not surprisingly, the pressure exerted by the vesicle on the wall depends on
the osmotic pressure inside, especially its sign. Here, we discuss the scaling
of this pressure in the different regimes, paying particular attention to the
crossover between positive and negative osmotic pressure. In our directed
model, there exists an underlying Airy function scaling form, from which we
extract the dependence of the bulk pressure on small osmotic pressures.Comment: 10 pages, 7 figure
Exact Solution of the Discrete (1+1)-dimensional RSOS Model in a Slit with Field and Wall Interactions
We present the solution of a linear Restricted Solid--on--Solid (RSOS) model
confined to a slit. We include a field-like energy, which equivalently weights
the area under the interface, and also include independent interaction terms
with both walls. This model can also be mapped to a lattice polymer model of
Motzkin paths in a slit interacting with both walls and including an osmotic
pressure. This work generalises previous work on the RSOS model in the
half-plane which has a solution that was shown recently to exhibit a novel
mathematical structure involving basic hypergeometric functions .
Because of the mathematical relationship between half-plane and slit this work
hence effectively explores the underlying -orthogonal polynomial structure
to that solution. It also generalises two other recent works: one on Dyck paths
weighted with an osmotic pressure in a slit and another concerning Motzkin
paths without an osmotic pressure term in a slit
The role of three-body interactions in two-dimensional polymer collapse
Various interacting lattice path models of polymer collapse in two dimensions
demonstrate different critical behaviours. This difference has been without a
clear explanation. The collapse transition has been variously seen to be in the
Duplantier-Saleur -point university class (specific heat cusp), the
interacting trail class (specific heat divergence) or even first-order. Here we
study via Monte Carlo simulation a generalisation of the Duplantier-Saleur
model on the honeycomb lattice and also a generalisation of the so-called
vertex-interacting self-avoiding walk model (configurations are actually
restricted trails known as grooves) on the triangular lattice. Crucially for
both models we have three and two body interactions explicitly and
differentially weighted. We show that both models have similar phase diagrams
when considered in these larger two-parameter spaces. They demonstrate regions
for which the collapse transition is first-order for high three body
interactions and regions where the collapse is in the Duplantier-Saleur
-point university class. We conjecture a higher order multiple critical
point separating these two types of collapse.Comment: 17 pages, 20 figure
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