PHASE TRANSITION OF A MODEL OF FLUID MEMBRANE

2000 ◽  
Vol 11 (03) ◽  
pp. 441-450 ◽  
Author(s):  
HIROSHI KOIBUCHI ◽  
MITSURU YAMADA
Keyword(s):  
Phase Transition ◽  
Piecewise Linear ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Bending Rigidity ◽  
Bending Energy ◽  
Random Surface ◽  
Spherical Surfaces ◽  
Fluid Membrane ◽  
Second Order Phase Transition

A model of fluid membrane, which is not self-avoiding, such as two-dimensional spherical random surface is studied by using Monte Carlo simulation. Spherical surfaces in R3 are discretized by piecewise linear triangle. Dynamical variables are the positions X of the vertices and the triangulation g. The action of the model is sum of area energy and bending energy times bending rigidity b. The bending energy and the specific heat are measured, and the critical exponents of the phase transitions are obtained by a finite-size scaling technique. We find that our model of fluid membrane undergoes a second order phase transition.

scholarly journals Компьютерное моделирование фазовых переходов и критических свойств фрустрированной модели Гейзенберга на кубической решетке

2020 ◽  
Vol 62 (6) ◽  
pp. 868
Author(s):  
М.К. Рамазанов ◽  
А.К. Муртазаев
Keyword(s):  
Phase Transition ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Universality Class ◽  
Critical Properties ◽  
Finite Size Scaling ◽  
Cubic Lattice ◽  
Range Of Values ◽  
Antiferromagnetic Model ◽  
Second Order Phase Transition

The phase transitions and critical properties of the Heisenberg antiferromagnetic model on a cubic lattice with nearest and next-nearest-neighbor interactions are investigated by the replica Monte Carlo method. The range of values of the interaction of the next-nearest-neighbor is considered 0.0 ≤ r ≤ 1.0. The phase diagram relating the transition temperature and the magnitude of next-nearest neighbor interactions is constructed. It is shown that a second order phase transition occurs in the r range under study. The values of all the main static critical exponents are calculated by means of the finite-size scaling theory. It is shown that the universality class of the critical behavior of this model is preserved in the range of 0.0 ≤ r ≤ 0.4.

The Investigation of Critical Properties of the Transition from Modulated Phase into Paramagnetic Phase

2015 ◽  
Vol 233-234 ◽  
pp. 30-33
Author(s):  
A.K. Murtazaev ◽  
Zhavrail G. Ibaev
Keyword(s):  
Phase Transition ◽  
Finite Size ◽  
Paramagnetic Phase ◽  
Critical Parameters ◽  
Critical Properties ◽  
Finite Size Scaling ◽  
Competing Interactions ◽  
Scaling Method ◽  
Modulated Phase ◽  
Second Order Phase Transition

The anisotropic Ising model with competing interactions in the region of transition from a modulated phase into paramagnetic state is investigated by the Monte-Carlo methods. By means of histogram analysis and the finite-size scaling method, the modulated – paramagnetic phase transition is shown to be a second order phase transition. Critical parameters and temperatures of phase transitions in this region are calculated.

THE SIMULATION OF 2D SPIN-1 ISING MODEL WITH POSITIVE BIQUADRATIC INTERACTION ON A CELLULAR AUTOMATON

2003 ◽  
Vol 14 (10) ◽  
pp. 1305-1320 ◽  
Author(s):  
BÜLENT KUTLU
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Cellular Automaton ◽  
Intermediate Phase ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Antiferromagnetic Spin

The two-dimensional antiferromagnetic spin-1 Ising model with positive biquadratic interaction is simulated on a cellular automaton which based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transition of the model are presented for a comparison with those obtained from other calculations. We confirm the existence of the intermediate phase observed in previous works for some values of J/K and D/K. The values of the static critical exponents (β, γ and ν) are estimated within the framework of the finite-size scaling theory for D/K<2J/K. Although the results are compatible with the universal Ising critical behavior in the region of D/K<2J/K-4, the model does not exhibit any universal behavior in the interval 2J/K-4<D/K<2J/K.

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