Monte Carlo simulations of branched polymer surfaces without bending elasticity

Koibuchi, Hiroshi; Nidaira, Atsusi; Morita, Takumi; Suzuki, Komei

doi:10.1103/physreve.68.011804

Cited by 10 publications

(22 citation statements)

References 27 publications

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“…2(b), respectively. H 200 and H tub slightly deviate from H = 2 which is confirmed in the case of branched polymer surfaces [26], where surfaces randomly stretch and hence are rotationally symmetric. Snapshots of N = 1000 surfaces are shown in Figs.…”

Section: Resultssupporting

confidence: 65%

Phase transitions of a tethered surface model with a deficit angle term

2004

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The 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 R3 . 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.

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Section: Resultssupporting

confidence: 65%

Phase transitions of a tethered surface model with a deficit angle term

2004

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“…(2) can make the surface smooth not only in the model with the Gaussian term but also in the Nambu-Goto surface model within the class of tethered surfaces [38]. Whereas the term S 3 (q) = − i log q i is constant on the tethered surfaces, and moreover the equivalent term S 3 (q) = i (q i − 6) 2 plays no role in smoothing fluid surfaces [37]. We therefore have discovered a significant difference for the role of S 3 (δ) in Eq.…”

Section: Model and Monte Carlo Techniquementioning

confidence: 99%

“…Studies have also focused on the phase structure of the model with intrinsic curvature [37,38,39,40,41]. It has been shown that the first-order transition can be seen in spherical fluid/tethered surfaces [38,39], tethered surface of disk topology [40], and tethered surface with torus topology [41].…”

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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“…A considerable number of studies have been conducted on the phase transition between the smooth phase and the crumpled one over the past two decades [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27 Curvature energies play a crucial role in smoothing the surface. According to curvature energies, surface models can be divided into two classes; one with an extrinsic curvature and the other with an intrinsic curvature.…”

Section: Introductionmentioning

confidence: 99%