Glass phase in anisotropic surface model for membranes

2nd International Conference on Mathematical Modeling in Physical Sciences 2013

物理学;数学

Koibuchi, Hiroshi^1 ; Shobukhov, Andrey^2

Ibaraki National College of Technology, Nakane 866, Ibaraki 312-8508 Hitachinaka, Japan^1

Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Leninskiye Gory, 119991, Moscow, Russia^2

关键词: Anisotropic surfaces;    Geometric surfaces;    Model Hamiltonians;    Monte carlo simulation technique;    Ordered configuration;    Random configurations;    Surface tension coefficient;    Three-dimensional units;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/490/1/012062/pdf
DOI  :  10.1088/1742-6596/490/1/012062

来源: IOP

【 摘 要 】

A Finsler geometric surface model for membranes is studied by using the Monte Carlo simulation technique on connection-fixed triangle lattices with sphere topology. An in-plane three-dimensional unit vector σ is assumed to be the in-plane tilt variable of the surface. The interaction with σ is described by the XY-model Hamiltonian. Since this variable σ is considered as a vector field on the surface, a Finsler metric is defined by using σ. We find that the model has three different phases. They change from the para-magnetic phase to the ferromagnetic and to the glass phases when the strength of the XY interaction increases. Both the para-magnetic and the glass phases are characterized by random configuration of σ; the variable σ randomly fluctuates in the para-magnetic phase while it is randomly frozen in the glass phase. We also find that the surface becomes spherical in both phases. On the contrary, in the ferro-magnetic phase the surface shape becomes tubular or discotic due to the anisotropic bending rigidity and surface tension coefficient, which are dynamically generated by ordered configurations of σ.