164 research outputs found
Shape transformation transitions of a tethered surface model
A surface model of Nambu and Goto is studied statistical mechanically by
using the canonical Monte Carlo simulation technique on a spherical meshwork.
The model is defined by the area energy term and a one-dimensional bending
energy term in the Hamiltonian. We find that the model has a large variety of
phases; the spherical phase, the planar phase, the long linear phase, the short
linear phase, the wormlike phase, and the collapsed phase. Almost all two
neighboring phases are separated by discontinuous transitions. It is also
remarkable that no surface fluctuation can be seen in the surfaces both in the
spherical phase and in the planar phase.Comment: 7 pages with 8 figure
Phase transitions in a fluid surface model with a deficit angle term
Nambu-Goto model is investigated by using the canonical Monte Carlo
simulation technique on dynamically triangulated surfaces of spherical
topology. We find that the model has four distinct phases; crumpled,
branched-polymer, linear, and tubular. The linear phase and the tubular phase
appear to be separated by a first-order transition. It is also found that there
is no long-range two-dimensional order in the model. In fact, no smooth surface
can be seen in the whole region of the curvature modulus \alpha, which is the
coefficient of the deficit angle term in the Hamiltonian. The bending energy,
which is not included in the Hamiltonian, remains large even at sufficiently
large \alpha in the tubular phase. On the other hand, the surface is
spontaneously compactified into a one-dimensional smooth curve in the linear
phase; one of the two degrees of freedom shrinks, and the other degree of
freedom remains along the curve. Moreover, we find that the rotational symmetry
of the model is spontaneously broken in the tubular phase just as in the same
model on the fixed connectivity surfaces.Comment: 8 pages with 10 figure
Phase transition of compartmentalized surface models
Two types of surface models have been investigated by Monte Carlo simulations
on triangulated spheres with compartmentalized domains. Both models are found
to undergo a first-order collapsing transition and a first-order surface
fluctuation transition. The first model is a fluid surface one. The vertices
can freely diffuse only inside the compartments, and they are prohibited from
the free diffusion over the surface due to the domain boundaries. The second is
a skeleton model. The surface shape of the skeleton model is maintained only by
the domain boundaries, which are linear chains with rigid junctions. Therefore,
we can conclude that the first-order transitions occur independent of whether
the shape of surface is mechanically maintained by the skeleton (= the domain
boundary) or by the surface itself.Comment: 10 pages with 16 figure
Phase structure of intrinsic curvature models on dynamically triangulated disk with fixed boundary length
A first-order phase transition is found in two types of intrinsic curvature
models defined on dynamically triangulated surfaces of disk topology. The
intrinsic curvature energy is included in the Hamiltonian. The smooth phase is
separated from a non-smooth phase by the transition. The crumpled phase, which
is different from the non-smooth phase, also appears at sufficiently small
curvature coefficient . The phase structure of the model on the disk is
identical to that of the spherical surface model, which was investigated by us
and reported previously. Thus, we found that the phase structure of the fluid
surface model with intrinsic curvature is independent of whether the surface is
closed or open.Comment: 9 pages with 10 figure
Grand Canonical simulations of string tension in elastic surface model
We report a numerical evidence that the string tension \sigma can be viewed
as an order parameter of the phase transition, which separates the smooth phase
from the crumpled one, in the fluid surface model of Helfrich and
Polyakov-Kleinert. The model is defined on spherical surfaces with two fixed
vertices of distance L. The string tension \sigma is calculated by regarding
the surface as a string connecting the two points. We find that the phase
transition strengthens as L is increased, and that \sigma vanishes in the
crumpled phase and non-vanishes in the smooth phase.Comment: 7 pages with 7 figure
Surface tension in an intrinsic curvature model with fixed one-dimensional boundaries
A triangulated fixed connectivity surface model is investigated by using the
Monte Carlo simulation technique. In order to have the macroscopic surface
tension \tau, the vertices on the one-dimensional boundaries are fixed as the
edges (=circles) of the tubular surface in the simulations. The size of the
tubular surface is chosen such that the projected area becomes the regular
square of area A. An intrinsic curvature energy with a microscopic bending
rigidity b is included in the Hamiltonian. We found that the model undergoes a
first-order transition of surface fluctuations at finite b, where the surface
tension \tau discontinuously changes. The gap of \tau remains constant at the
transition point in a certain range of values A/N^\prime at sufficiently large
N^\prime, which is the total number of vertices excluding the fixed vertices on
the boundaries. The value of \tau remains almost zero in the wrinkled phase at
the transition point while \tau remains negative finite in the smooth phase in
that range of A/N^\prime.Comment: 12 pages, 8 figure
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
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