134 research outputs found
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
Scaling function and universal amplitude combinations for self-avoiding polygons
We analyze new data for self-avoiding polygons, on the square and triangular
lattices, enumerated by both perimeter and area, providing evidence that the
scaling function is the logarithm of an Airy function. The results imply
universal amplitude combinations for all area moments and suggest that rooted
self-avoiding polygons may satisfy a -algebraic functional equation.Comment: 9 page
Monte Carlo Investigation of Lattice Models of Polymer Collapse in Five Dimensions
Monte Carlo simulations, using the PERM algorithm, of interacting
self-avoiding walks (ISAW) and interacting self-avoiding trails (ISAT) in five
dimensions are presented which locate the collapse phase transition in those
models. It is argued that the appearance of a transition (at least) as strong
as a pseudo-first-order transition occurs in both models. The values of various
theoretically conjectured dimension-dependent exponents are shown to be
consistent with the data obtained. Indeed the first-order nature of the
transition is even stronger in five dimensions than four. The agreement with
the theory is better for ISAW than ISAT and it cannot be ruled out that ISAT
have a true first-order transition in dimension five. This latter difference
would be intriguing if true. On the other hand, since simulations are more
difficult for ISAT than ISAW at this transition in high dimensions, any
discrepancy may well be due to the inability of the simulations to reach the
true asymptotic regime.Comment: LaTeX file, 16 pages incl. 7 figure
On the location of the surface-attached globule phase in collapsing polymers
We investigate the existence and location of the surface phase known as the
"Surface-Attached Globule" (SAG) conjectured previously to exist in lattice
models of three-dimensional polymers when they are attached to a wall that has
a short range potential. The bulk phase, where the attractive intra-polymer
interactions are strong enough to cause a collapse of the polymer into a
liquid-like globule and the wall either has weak attractive or repulsive
interactions, is usually denoted Desorbed-Collapsed or DC. Recently this DC
phase was conjectured to harbour two surface phases separated by a boundary
where the bulk free energy is analytic while the surface free energy is
singular. The surface phase for more attractive values of the wall interaction
is the SAG phase. We discuss more fully the properties of this proposed surface
phase and provide Monte Carlo evidence for self-avoiding walks up to length 256
that this surface phase most likely does exist. Importantly, we discuss
alternatives for the surface phase boundary. In particular, we conclude that
this boundary may lie along the zero wall interaction line and the bulk phase
boundaries rather than any new phase boundary curve.Comment: slightly extended versio
Exact Solution of Semi-Flexible and Super-Flexible Interacting Partially Directed Walks
We provide the exact generating function for semi-flexible and super-flexible
interacting partially directed walks and also analyse the solution in detail.
We demonstrate that while fully flexible walks have a collapse transition that
is second order and obeys tricritical scaling, once positive stiffness is
introduced the collapse transition becomes first order. This confirms a recent
conjecture based on numerical results. We note that the addition of an
horizontal force in either case does not affect the order of the transition. In
the opposite case where stiffness is discouraged by the energy potential
introduced, which we denote the super-flexible case, the transition also
changes, though more subtly, with the crossover exponent remaining unmoved from
the neutral case but the entropic exponents changing
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