Monte Carlo simulations of Landau–Ginzburg model for membranes

Hiroshi Koibuchi () and Andrey Shobukhov
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Hiroshi Koibuchi: Department of Mechanical and Systems Engineering, Ibaraki National College of Technology, Nakane 866 Hitachinaka, Ibaraki 312-8508, Japan
Andrey Shobukhov: Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991, Moscow, Leninskiye Gory, MSU, 2nd Educational Building, Russia

International Journal of Modern Physics C (IJMPC), 2014, vol. 25, issue 08, 1-18

Abstract: The Landau–Ginzburg (LG) model for membranes is numerically studied on triangulated spheres inR3. The LG model is in sharp contrast to the model of Helfrich–Polyakov (HP). The reason for this difference is that the curvature energy of the LG (HP) Hamiltonian is defined by means of the tangential (normal) vector of the surface. For this reason, the curvature energy of the LG model includes the in-plane bending or shear energy component, which is not included in the curvature energy of the HP model. From the simulation data, we find that the LG model undergoes a first-order collapse transition. The results of the LG model in the higher-dimensional spacesRd(d > 3)and on the self-avoiding (SA) surfaces inR3are presented and discussed. We also study the David–Guitter (DG) model, which is a variant of the LG model, and find that the DG model undergoes a first-order transition. It is also found that the transition can be observed only on the homogeneous surfaces, which are composed of almost uniform triangles according to the condition that the induced metric∂ar⋅ ∂bris close toδab.

Keywords: Surface model; Landau–Ginzburg; phase transition; surface metric; 64.60.-i; 68.60.-p; 87.10.-e; 87.16.D- (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1142/S0129183114500338

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