Monte Carlo simulations of tensionless membranes

Koibuchi, Hiroshi; Kusano, Nobuyuki; Nidaira, Atsusi; Suzuki, Komei; Suzuki, Takanori

doi:10.1016/s0375-9601(03)00771-0

Cited by 7 publications

(13 citation statements)

References 36 publications

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“…Figures 6 (c) and 6 (d) show the results of Model-2. There is no difference between the surfaces in the smooth phase of the models in this paper and those of [15]. While the surfaces in the disordered (or crumpled) phase of the models in this paper are more crumpled than those in [15].…”

Section: Model and MC Techniquesmentioning

confidence: 64%

“…The histograms of coordination number of surfaces are identical with those shown in Ref. [15]. The position X of vertices is updated in MC by moving the current position X to a new position X ′ = X+δX, where δX is chosen in a small sphere by using uniform random numbers.…”

Section: Model and MC Techniquesmentioning

confidence: 98%

“…However, little attention has been given to the dependence of the phase transition on the Hamiltonian of tethered surfaces both for models that have surface tension [12,13,14,15,16,17,18,19,20,21] and for tensionless models [22,23,24,25,26,27]. Almost all numerical studies done so far utilize the bending energy of the ordinary form 1−n i · n j , where n i is the normal vector of the triangle i.…”

Section: Introductionmentioning

confidence: 99%

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First-order phase transition of fixed connectivity surfaces

et al. 2004

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We report a numerical evidence of the discontinuous transition of a tethered membrane model which is defined within a framework of the membrane elasticity of Helfrich. Two kinds of phantom tethered membrane models are studied via the canonical Monte Carlo simulation on triangulated fixed connectivity surfaces of spherical topology. A surface model is defined by the Gaussian term and the bending energy term, and the other, which is tensionless, is defined by the bending energy term and a hard wall potential. The bending energy is defined by using the normal vector at each vertex. Both of the models undergo the first-order phase transition characterized by a gap of the bending energy. The phase structure of the models depends on the choice of discrete bending energy.

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Section: Model and MC Techniquesmentioning

confidence: 64%

Section: Model and MC Techniquesmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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First-order phase transition of fixed connectivity surfaces

et al. 2004

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“…Tethered surface models are defined on triangulated fixed connectivity surfaces representing polymerized biological membranes or membranes in the gel phase [7], and they are classified into a major class of the HPK model [15,16,17,18,19,20,21,22,23,24,25,26]. Fluid surface models are considered a different class of the HPK model defined on dynamically triangulated surfaces representing these biological membranes in the fluid phase, however, we will not discuss the fluid surface model in this paper [27,28,29,30,31,32,33,34].…”

Section: Introductionmentioning

confidence: 99%

First-order phase transition of the tethered membrane model on spherical surfaces

Endo

Koibuchi

2006

Nuclear Physics B

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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.

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“…The surface models can be classified into two groups, which are characterized by the curvature energy in the Hamiltonian; one is an extrinsic curvature model [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32], and the other is an intrinsic curvature model [33,34,35,36]. The extrinsic curvature model is known to undergo a first-order transition between the smooth phase and the crumpled phase on tethered spherical surfaces [22,23,24].…”

Section: Introductionmentioning

confidence: 99%

Phase transitions of a tethered membrane model with intrinsic curvature on spherical surfaces with point boundaries

Koibuchi¹

2006

J. Stat. Mech.

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Abstract. We found that the order for the crumpling transition of an intrinsic curvature model changes depending on the distance between two boundary vertices fixed on the surface of spherical topology. The model is a curvature one governed by an intrinsic curvature energy, which is defined on triangulated surfaces. It was already reported that the model undergoes a first-order crumpling transition without the boundary conditions on the surface. However, the dependence of the transition on such boundary condition is yet to be studied. We have studied in this paper this problem by using the Monte Carlo simulations on surfaces up to a size N = 8412. The first-order transition changes to a second-order one if the distance increases.

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Monte Carlo simulations of tensionless membranes

Cited by 7 publications

References 36 publications

First-order phase transition of fixed connectivity surfaces

First-order phase transition of fixed connectivity surfaces

First-order phase transition of the tethered membrane model on spherical surfaces

Phase transitions of a tethered membrane model with intrinsic curvature on spherical surfaces with point boundaries

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