141 research outputs found
First-order phase transition in the tethered surface model on a sphere
We show that the tethered surface model of Helfrich and Polyakov-Kleinert
undergoes a first-order phase transition separating the smooth phase from the
crumpled one. The model is investigated by the canonical Monte Carlo
simulations on spherical and fixed connectivity surfaces of size up to N=15212.
The first-order transition is observed when N>7000, which is larger than those
in previous numerical studies, and a continuous transition can also be observed
on small-sized surfaces. Our results are, therefore, consistent with those
obtained in previous studies on the phase structure of the model.Comment: 6 pages with 7 figure
Phase transitions of a tethered surface model with a deficit angle term
Nambu-Goto model is investigated by using the canonical Monte Carlo
simulations on fixed connectivity surfaces of spherical topology. Three
distinct phases are found: crumpled, tubular, and smooth. The crumpled and the
tubular phases are smoothly connected, and the tubular and the smooth phases
are connected by a discontinuous transition. The surface in the tubular phase
forms an oblong and one-dimensional object similar to a one-dimensional linear
subspace in the Euclidean three-dimensional space R^3. This indicates that the
rotational symmetry inherent in the model is spontaneously broken in the
tubular phase, and it is restored in the smooth and the crumpled phases.Comment: 6 pages with 6 figure
Phase transition of triangulated spherical surfaces with elastic skeletons
A first-order transition is numerically found in a spherical surface model
with skeletons, which are linked to each other at junctions. The shape of the
triangulated surfaces is maintained by skeletons, which have a one-dimensional
bending elasticity characterized by the bending rigidity , and the surfaces
have no two-dimensional bending elasticity except at the junctions. The
surfaces swell and become spherical at large and collapse and crumple at
small . These two phases are separated from each other by the first-order
transition. Although both of the surfaces and the skeleton are allowed to
self-intersect and, hence, phantom, our results indicate a possible phase
transition in biological or artificial membranes whose shape is maintained by
cytoskeletons.Comment: 15 pages with 10 figure
Phase transition of meshwork models for spherical membranes
We have studied two types of meshwork models by using the canonical Monte
Carlo simulation technique. The first meshwork model has elastic junctions,
which are composed of vertices, bonds, and triangles, while the second model
has rigid junctions, which are hexagonal (or pentagonal) rigid plates.
Two-dimensional elasticity is assumed only at the elastic junctions in the
first model, and no two-dimensional bending elasticity is assumed in the second
model. Both of the meshworks are of spherical topology. We find that both
models undergo a first-order collapsing transition between the smooth spherical
phase and the collapsed phase. The Hausdorff dimension of the smooth phase is
H\simeq 2 in both models as expected. It is also found that H\simeq 2 in the
collapsed phase of the second model, and that H is relatively larger than 2 in
the collapsed phase of the first model, but it remains in the physical bound,
i.e., H<3. Moreover, the first model undergoes a discontinuous surface
fluctuation transition at the same transition point as that of the collapsing
transition, while the second model undergoes a continuous transition of surface
fluctuation. This indicates that the phase structure of the meshwork model is
weakly dependent on the elasticity at the junctions.Comment: 21 pages, 12 figure
Collapsing transition of spherical tethered surfaces with many holes
We investigate a tethered (i.e. fixed connectivity) surface model on
spherical surfaces with many holes by using the canonical Monte Carlo
simulations. Our result in this paper reveals that the model has only a
collapsing transition at finite bending rigidity, where no surface fluctuation
transition can be seen. The first-order collapsing transition separates the
smooth phase from the collapsed phase. Both smooth and collapsed phases are
characterized by Hausdorff dimension H\simeq 2, consequently, the surface
becomes smooth in both phases. The difference between these two phases can be
seen only in the size of surface. This is consistent with the fact that we can
see no surface fluctuation transition at the collapsing transition point. These
two types of transitions are well known to occur at the same transition point
in the conventional surface models defined on the fixed connectivity surfaces
without holes.Comment: 7 pages with 11 figure
Spherical surface models with directors
A triangulated spherical surface model is numerically studied, and it is
shown that the model undergoes phase transitions between the smooth phase and
the collapsed phase. The model is defined by using a director field, which is
assumed to have an interaction with a normal of the surface. The interaction
between the directors and the surface maintains the surface shape. The director
field is not defined within the two-dimensional differential geometry, and this
is in sharp contrast to the conventional surface models, where the surface
shape is maintained only by the curvature energies. We also show that the
interaction makes the Nambu-Goto model well-defined, where the bond potential
is given by the area of triangles; the Nambu-Goto model is well-known as an
ill-defined one even when the conventional two-dimensional bending energy is
included in the Hamiltonian.Comment: 18 pages, 13 figure
In-plane deformation of a triangulated surface model with metric degrees of freedom
Using the canonical Monte Carlo simulation technique, we study a Regge
calculus model on triangulated spherical surfaces. The discrete model is
statistical mechanically defined with the variables , and , which
denote the surface position in , the metric on a two-dimensional
surface and the surface density of , respectively. The metric is
defined only by using the deficit angle of the triangles in {}. This is in
sharp contrast to the conventional Regge calculus model, where {} depends
only on the edge length of the triangles. We find that the discrete model in
this paper undergoes a phase transition between the smooth spherical phase at
and the crumpled phase at , where is the bending
rigidity. The transition is of first-order and identified with the one observed
in the conventional model without the variables and . This implies
that the shape transformation transition is not influenced by the metric
degrees of freedom. It is also found that the model undergoes a continuous
transition of in-plane deformation. This continuous transition is reflected in
almost discontinuous changes of the surface area of and that of ,
where the surface area of is conjugate to the density variable .Comment: 13 pages, 7 figure
Phase transitions of an intrinsic curvature model on dynamically triangulated spherical surfaces with point boundaries
An intrinsic curvature model is investigated using the canonical Monte Carlo
simulations on dynamically triangulated spherical surfaces of size upto N=4842
with two fixed-vertices separated by the distance 2L. We found a first-order
transition at finite curvature coefficient \alpha, and moreover that the order
of the transition remains unchanged even when L is enlarged such that the
surfaces become sufficiently oblong. This is in sharp contrast to the known
results of the same model on tethered surfaces, where the transition weakens to
a second-order one as L is increased. The phase transition of the model in this
paper separates the smooth phase from the crumpled phase. The surfaces become
string-like between two point-boundaries in the crumpled phase. On the
contrary, we can see a spherical lump on the oblong surfaces in the smooth
phase. The string tension was calculated and was found to have a jump at the
transition point. The value of \sigma is independent of L in the smooth phase,
while it increases with increasing L in the crumpled phase. This behavior of
\sigma is consistent with the observed scaling relation \sigma \sim (2L/N)^\nu,
where \nu\simeq 0 in the smooth phase, and \nu=0.93\pm 0.14 in the crumpled
phase. We should note that a possibility of a continuous transition is not
completely eliminated.Comment: 15 pages with 10 figure
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