The phase diagram of crystalline surfaces

Anagnostopoulos, Konstantinos N.; Bowick, Mark J.; Catterall, Simon; Falcioni, M.; Þorleifsson, Guðmar

doi:10.1016/0920-5632(96)00187-9

Cited by 17 publications

(6 citation statements)

References 19 publications

(22 reference statements)

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“…(11) gives H 2 if the surface is smooth. The fitted values of H are H = 2.33(7) at b = 0.125, H = 2.57(2) at b = 0.123 and H = 3.14(9) at b = 0.121.…”

Section: Monte Carlo Simulationmentioning

confidence: 99%

“…[6][7][8][9][10][11][12] The dynamical variables of a model of fluid membrane are the position X of molecules (vertices of triangles) and the triangulation (flips of bonds). On the other hand, a crystalline membrane model has only X as its dynamical variable.…”

Section: Introduction and The Modelmentioning

confidence: 99%

“…On the other hand, a crystalline membrane model has only X as its dynamical variable. [6][7][8][9][10][11][12] The crystalline membrane in this paper is a fixed connectivity model with a discretized Helfrich bending energy. This definition is identical with the one used in Refs.…”

Section: Introduction and The Modelmentioning

confidence: 99%

“…This definition is identical with the one used in Refs. [6][7][8][9][10][11][12]. The deformation of shape of the crystalline membrane is caused by motions of the molecules in R 3 .…”

Section: Introduction and The Modelmentioning

confidence: 99%

“…13 It is well-known that there is a second order phase transition of a crystalline membrane with the Helfrich energy. [6][7][8][9][10][11][12] However, it is still not so clear whether the fluid membrane, which is a dynamically triangulated surface with the discretized Helfrich bending energy, undergoes the second order phase transition or not. We find from Refs.…”

Section: Introduction and The Modelmentioning

confidence: 99%

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Phase Transition of a Model of Crystalline Membrane

Koibuchi

Yamada

2000

Int. J. Mod. Phys. C

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We study two-dimensional triangulated surfaces of sphere topology by the canonical Monte Carlo simulation. The coordination number of surfaces is made as uniform as possible. The triangulation is fixed in MC so that only the positions X of vertices may be considered as the dynamical variable. The well-known Helfrich energy function S = S 1 + bS 2 is used for the definition of the model where S 1 and S 2 are the area and bending energy functions respectively and b is the bending rigidity. The discretizations of S 1 and S 2 are identical with that of our previous MC study for a model of fluid membranes. We find that the specific heats have peaks at finite bending rigidities and obtain the critical exponents of the phase transition by the finite-size scaling technique. It is found that our model of crystalline membranes undergoes an expected second order phase transition.

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“…(11) gives H 2 if the surface is smooth. The fitted values of H are H = 2.33(7) at b = 0.125, H = 2.57(2) at b = 0.123 and H = 3.14(9) at b = 0.121.…”

Section: Monte Carlo Simulationmentioning

confidence: 99%

Section: Introduction and The Modelmentioning

confidence: 99%

Section: Introduction and The Modelmentioning

confidence: 99%

“…This definition is identical with the one used in Refs. [6][7][8][9][10][11][12]. The deformation of shape of the crystalline membrane is caused by motions of the molecules in R 3 .…”

Section: Introduction and The Modelmentioning

confidence: 99%

Section: Introduction and The Modelmentioning

confidence: 99%

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Phase Transition of a Model of Crystalline Membrane

Koibuchi

Yamada

2000

Int. J. Mod. Phys. C

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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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