Landau Theory of the Crumpling Transition

Paczuski, Maya; Kardar, Mehran; Nelson, David R.

doi:10.1103/physrevlett.60.2638

Cited by 185 publications

(269 citation statements)

References 9 publications

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“…A simple Flory-type argument, which takes into account self-avoidance, predicts the fractal dimension D f ¼ 5=2 [40,60]. The crumpling transition at high temperatures was in fact observed in Monte Carlo simulations of phantom membranes without self-avoidance [61,62].…”

Section: Introductionmentioning

confidence: 99%

Statistical Mechanics of Thin Spherical Shells

Košmrlj

Nelson

2017

Phys. Rev. X

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We explore how thermal fluctuations affect the mechanics of thin amorphous spherical shells. In flat membranes with a shear modulus, thermal fluctuations increase the bending rigidity and reduce the inplane elastic moduli in a scale-dependent fashion. This is still true for spherical shells. However, the additional coupling between the shell curvature, the local in-plane stretching modes, and the local out-ofplane undulations leads to novel phenomena. In spherical shells, thermal fluctuations produce a radiusdependent negative effective surface tension, equivalent to applying an inward external pressure. By adapting renormalization group calculations to allow for a spherical background curvature, we show that while small spherical shells are stable, sufficiently large shells are crushed by this thermally generated "pressure." Such shells can be stabilized by an outward osmotic pressure, but the effective shell size grows nonlinearly with increasing outward pressure, with the same universal power-law exponent that characterizes the response of fluctuating flat membranes to a uniform tension.

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Section: Introductionmentioning

confidence: 99%

Statistical Mechanics of Thin Spherical Shells

Košmrlj

Nelson

2017

Phys. Rev. X

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“…Over the past two decades, a considerable number of studies have been performed on the phase structure of the surface model of Helfrich [1], Polyakov [2], and Kleinert [3] for biological membranes [4,5,6,7,8,9,10,11,12,13,14]. 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].…”

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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“…Models of polymerized membranes were introduced in [7], and studied using a LandauGinzburg evaluation of the energy of the system in [4,8,9,10]. From the above studies, and from numerical simulations [11], it comes out that, when excluded volume effects are not considered, by varying the strength K of a bending energy term which favours flat configurations, a critical transition arises separating a flat phase at large K from a crumpled phase at small K.…”

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Folding transition of the triangular lattice in a discrete three-dimensional space

1996

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A vertex model introduced by M. Bowick, P. Di Francesco, O. Golinelli, and E. Guitter [Nucl. Phys. B 450, 463 (1995)] describing the folding of the triangular lattice onto the face centered cubic lattice has been studied in the hexagon approximation of the cluster variation method. The model describes the behaviour of a polymerized membrane in a discrete three-dimensional space. We have introduced a curvature energy and a symmetry breaking field and studied the phase diagram of the resulting model. By varying the curvature energy parameter, a first-order transition has been found between a flat and a folded phase for any value of the symmetry breaking field.PACS numbers: 05.50.+q (Ising problems); 64.60.-i (General studies of phase transitions); 82.65.Dp (Thermodynamics of surfaces and interfaces).

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Landau Theory of the Crumpling Transition

Cited by 185 publications

References 9 publications

Statistical Mechanics of Thin Spherical Shells

Statistical Mechanics of Thin Spherical Shells

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

Folding transition of the triangular lattice in a discrete three-dimensional space

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