795 research outputs found
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
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 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
First-order phase transition of the tethered membrane model on spherical surfaces
We found that three types of tethered surface model undergo a first-order
phase transition between the smooth and the crumpled phase. The first and the
third are discrete models of Helfrich, Polyakov, and Kleinert, and the second
is that of Nambu and Goto. These are curvature models for biological membranes
including artificial vesicles. The results obtained in this paper indicate that
the first-order phase transition is universal in the sense that the order of
the transition is independent of discretization of the Hamiltonian for the
tethered surface model.Comment: 22 pages with 14 figure
Phase transitions of a tethered membrane model on a torus with intrinsic curvature
A tethered surface model is investigated by using the canonical Monte Carlo
simulation technique on a torus with an intrinsic curvature. We find that the
model undergoes a first-order phase transition between the smooth phase and the
crumpled one.Comment: 12 pages with 8 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 a spherical surface model on fixed connectivity meshes
An elastic surface model is investigated by using the canonical Monte Carlo
simulation technique on triangulated spherical meshes. The model undergoes a
first-order collapsing transition and a continuous surface fluctuation
transition. The shape of surfaces is maintained by a one-dimensional bending
energy, which is defined on the mesh, and no two-dimensional bending energy is
included in the Hamiltonian.Comment: 13 pages with 9 figure
Phase transition of an extrinsic curvature model on tori
We show a numerical evidence that a tethered surface model with extrinsic
curvature undergoes a first-order crumpling transition between the smooth phase
and a non-smooth phase on triangulated tori. The results obtained in this
Letter together with the previous ones on spherical surfaces lead us to
conclude that the tethered surface model undergoes a first-order transition on
compact surfaces.Comment: 13 pages with 10 figure
Shape transformation transitions in a model of fixed-connectivity surfaces supported by skeletons
A compartmentalized surface model of Nambu and Goto is studied on
triangulated spherical surfaces by using the canonical Monte Carlo simulation
technique. One-dimensional bending energy is defined on the skeletons and at
the junctions, and the mechanical strength of the surface is supplied by the
one-dimensional bending energy defined on the skeletons and junctions. The
compartment size is characterized by the total number L^\prime of bonds between
the two-neighboring junctions and is assumed to have values in the range from
L^\prime=2 to L^\prime=8 in the simulations, while that of the previously
reported model is characterized by L^\prime=1, where all vertices of the
triangulated surface are the junctions. Therefore, the model in this paper is
considered to be an extension of the previous model in the sense that the
previous model is obtained from the model in this paper in the limit of
L^\prime\to1 The model in this paper is identical to the Nambu-Goto surface
model without curvature energies in the limit of L^\prime\to \infty and hence
is expected to be ill-defined at sufficiently large L^\prime. One remarkable
result obtained in this paper is that the model has a well-defined smooth phase
even at relatively large L^\prime just as the previous model of L^\prime\to1.
It is also remarkable that the fluctuations of surface in the smooth phase are
crucially dependent on L^\prime; we can see no surface fluctuation when
L^\prime\leq2, while relatively large fluctuations are seen when L^\prime\geq3.Comment: 7 pages, 8 figure
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