scholarly journals Parallel Tempering Monte Carlo Studies of Phase Transition of Free Boundary Planar Surfaces

Polymers ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 1360
Author(s):  
Andrey Shobukhov ◽  
Hiroshi Koibuchi
Keyword(s):  
Monte Carlo ◽  
Free Boundary ◽  
Functional Materials ◽  
Thermal Fluctuations ◽  
Order Transition ◽  
Parallel Tempering ◽  
First Order ◽  
Planar Surfaces ◽  
Surface Models ◽  
First Order Transition

We numerically study surface models defined on hexagonal disks with a free boundary. 2D surface models for planar surfaces have recently attracted interest due to the engineering applications of functional materials such as graphene and its composite with polymers. These 2D composite meta-materials are strongly influenced by external stimuli such as thermal fluctuations if they are sufficiently thin. For this reason, it is very interesting to study the shape stability/instability of thin 2D materials against thermal fluctuations. In this paper, we study three types of surface models including Landau-Ginzburg (LG) and Helfirch-Polyakov models defined on triangulated hexagonal disks using the parallel tempering Monte Carlo simulation technique. We find that the planar surfaces undergo a first-order transition between the smooth and crumpled phases in the LG model and continuous transitions in the other two models. The first-order transition is relatively weak compared to the transition on spherical surfaces already reported. The continuous nature of the transition is consistent with the reported results, although the transitions are stronger than that of the reported ones.

scholarly journals Parallel Tempering Monte Carlo Studies of Phase Transition of Free Boundary Planar Surfaces

2018 ◽  
Author(s):  
Andrey Shobukhov ◽  
Hiroshi Koibuchi
Keyword(s):  
Monte Carlo ◽  
Free Boundary ◽  
Functional Materials ◽  
Thermal Fluctuations ◽  
Order Transition ◽  
Parallel Tempering ◽  
First Order ◽  
Monte Carlo Studies ◽  
Surface Models ◽  
First Order Transition

We numerically study surface models defined on hexagonal disks with a free boundary. 2D surface models for planer surfaces have recently attracted interest due to the engineering applications of functional materials such as graphene and its composite with polymers. These 2D composite meta-materials are strongly influenced by external stimuli such as thermal fluctuations if they are sufficiently thin. For this reason, it is very interesting to study the shape stability/instability of thin 2D materials against thermal fluctuations. In this paper, we study three types of surface models including Landau-Ginzburg (LG) and Helfirch-Polyakov models defined on triangulated hexagonal disks using the parallel tempering Monte Carlo simulation technique. We find that the planer surfaces undergo a first-order transition between the smooth and crumpled phases in the LG model and continuous transitions in the other two models. The first-order transition is relatively weaker compared to the transition on spherical surfaces already reported. The continuous nature of the transition is consistent with the reported results, although the transitions are stronger than that of the reported ones.

scholarly journals MONTE CARLO INVESTIGATION OF LATTICE MODELS OF POLYMER COLLAPSE IN FIVE DIMENSIONS

2003 ◽  
Vol 14 (05) ◽  
pp. 621-633 ◽  
Author(s):  
A. L. OWCZAREK ◽  
T. PRELLBERG
Keyword(s):  
Monte Carlo ◽  
Lattice Models ◽  
Order Transition ◽  
High Dimensions ◽  
Five Dimensions ◽  
First Order ◽  
Polymer Collapse ◽  
Monte Carlo Investigation ◽  
First Order Transition ◽  
Self Avoiding Walks

Monte Carlo simulations, using the PERM algorithm, of interacting self-avoiding walks (ISAW) and interacting self-avoiding trails (ISAT) in five dimensions are presented which locate the collapse phase transition in those models. It is argued that the appearance of a transition (at least) as strong as a pseudo-first-order transition occurs in both models. The values of various theoretically-conjectured dimension-dependent exponents are shown to be consistent with the data obtained. Indeed the first-order nature of the transition is even stronger in five dimensions than four. The agreement with the theory is better for ISAW than ISAT and it cannot be ruled out that ISAT have a true first-order transition in dimension five. This latter difference would be intriguing if true. On the other hand, since simulations are more difficult for ISAT than ISAW at this transition in high dimensions, any discrepancy may well be due to the inability of the simulations to reach the true asymptotic regime.

scholarly journals SPIN RESISTIVITY IN THE FRUSTRATED J1 - J2 MODEL

2011 ◽  
Vol 25 (12n13) ◽  
pp. 937-945 ◽  
Author(s):  
DANH-TAI HOANG ◽  
YANN MAGNIN ◽  
H. T. DIEP
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Nearest Neighbors ◽  
Order Transition ◽  
Ising Lattice ◽  
First Order ◽  
Simple Cubic ◽  
First Order Transition ◽  
Dependent Interaction

We study in this paper the resistivity encountered by Ising itinerant spins traveling in the so-called J1 - J2 frustrated simple cubic Ising lattice. For the lattice, we take into account the interactions between nearest-neighbors and next-nearest-neighbors, J1 and J2 respectively. Itinerant spins interact with lattice spins via a distance-dependent interaction. We also take into account an interaction between itinerant spins. The lattice is frustrated in a range of J2 in which we show that it undergoes a very strong first-order transition. Using Monte Carlo simulation, we calculate the resistivity ρ of the itinerant spins and show that the first-order transition of the lattice causes a discontinuity of ρ.

MICROCANONICAL MONTE CARLO STUDY OF FIRST-ORDER TRANSITION IN A 2D CLASSICAL XY-MODEL

2007 ◽  
Vol 21 (20) ◽  
pp. 3591-3600 ◽  
Author(s):  
SMITA OTA ◽  
SNEHADRI BIHARI OTA
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Study ◽  
System Size ◽  
Order Transition ◽  
Xy Model ◽  
Statistical System ◽  
Simple Method ◽  
First Order ◽  
First Order Transition ◽  
Neighbour Interaction

The microcanonical ensemble given by Boltzmann is used in the computer Monte Carlo simulation of 2D classical XY-model with the modified nearest neighbour interaction potential suggested by Domany, Schick and Swendsen. A relatively simple method to identify first-order transition in computer simulations of a statistical system is described. The critical value of p2 in this XY-model is determined using this method; which is found to increase with system size obeying a power law.

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