BIASED DIFFUSION: TRAP ANALYSIS IN TWO DIMENSIONS

1999 ◽  
Vol 10 (04) ◽  
pp. 753-757 ◽  
Author(s):  
ALEXANDER KIRSCH
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Random Walk ◽  
Percolation Threshold ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Biased Diffusion

A method for analyzing clusters which block the random walk of particles in two-dimensional biased diffusion on percolation lattices above the percolation threshold pc is presented, focusing on the arising problems and explaining the phase transition. The difficulties in a precise trap definition are illustrated. Different trap definitions result in different trap statistics, more or less capable of capturing the trend of the phase diagram.

Phase Transition in Two-Dimensional Biased Diffusion

1998 ◽  
Vol 09 (07) ◽  
pp. 1021-1024 ◽  
Author(s):  
Alexander Kirsch
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Drift Velocity ◽  
Time Behavior ◽  
Two Dimensional ◽  
Long Time Behavior ◽  
Long Time ◽  
Biased Diffusion

We investigate the long-time behavior of the drift velocity of two-dimensional biased diffusion with varying bias B and percentage p of allowed sites. A phase diagram for the drift/no-drift transition depending on B and p is presented.

THE GROUNDSTATES AND PHASES OF THE TWO-DIMENSIONAL FULLY FRUSTRATED XY MODEL

2009 ◽  
Vol 23 (20n21) ◽  
pp. 3939-3950
Author(s):  
PETTER MINNHAGEN ◽  
SEBASTIAN BERNHARDSSON ◽  
BEOM JUN KIM
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Phase Transitions ◽  
Xy Model ◽  
Two Dimensional ◽  
Spin Configuration ◽  
Multicritical Points ◽  
Symmetry Phase

The 2D Fully Frustrated XY(FFXY) class of models is shown to contain a new groundstate in addition to the checkerboard groundstate of the standard 2D XY model. The spin configuration of this additional groundstate is obtained and its connection to a broken Z2-symmetry explained. This means that the class of 2D FFXY models belongs within a U(1) ⊗ Z2 ⊗ Z2-symmetry phase-transition representation. The phase diagram is reviewed and the central charges of the four multicritical points described. The implications for the standard 2D FFXY-model are discussed and elucidated, in particular with respect to the long standing controversy concerning the phase transitions of the standard 2D FFXY-model.

Phase Transition in 2D Anisotropic Ising Model with Next-Nearest Neighbor Interactions in a Magnetic Field

SPIN ◽  
2018 ◽  
Vol 08 (03) ◽  
pp. 1850010
Author(s):  
D. Farsal ◽  
M. Badia ◽  
M. Bennai
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
Phase Diagram ◽  
Monte Carlo ◽  
Magnetic Susceptibility ◽  
Critical Temperature ◽  
Ising Model ◽  
Nearest Neighbor ◽  
Two Dimensional ◽  
The Magnetic Field

The critical behavior at the phase transition of the ferromagnetic two-dimensional anisotropic Ising model with next-nearest neighbor (NNN) couplings in the presence of the field is determined using mainly Monte Carlo (MC) method. This method is used to investigate the phase diagram of the model and to verify the existence of a divergence at null temperature which often appears in two-dimensional systems. We analyze also the influence of the report of the NNN interactions [Formula: see text] and the magnetic field [Formula: see text] on the critical temperature of the system, and we show that the critical temperature depends on the magnetic field for positive values of the interaction. Finally, we have investigated other thermodynamical qualities such as the magnetic susceptibility [Formula: see text]. It has been shown that their thermal behavior depends qualitatively and quantitatively on the strength of NNN interactions and the magnetic field.

A first-passage problem for a two-dimensional controlled random walk

1986 ◽  
Vol 23 (3) ◽  
pp. 670-678
Author(s):  
S. Lalley
Keyword(s):  
Random Walk ◽  
First Passage Time ◽  
Passage Time ◽  
Two Dimensions ◽  
Main Diagonal ◽  
Two Dimensional ◽  
First Passage ◽  
Explicit Representations ◽  
Mean Vectors ◽  
First Passage Problem

The process of interest is a controlled random walk in two dimensions: whenever the walker is above the main diagonal, the next increment to his position is chosen from a distribution FA; whenever the walker is below the diagonal, the next increment comes from another distribution FB. The two distributions have mean vectors which tend to push the walker back toward the diagonal. We analyze the problem of first passage to the first quadrant, obtaining explicit representations for the limiting first-entry distribution and expected first-passage time.

A first-passage problem for a two-dimensional controlled random walk

1986 ◽  
Vol 23 (03) ◽  
pp. 670-678
Author(s):  
S. Lalley
Keyword(s):  
Random Walk ◽  
First Passage Time ◽  
Passage Time ◽  
Two Dimensions ◽  
Main Diagonal ◽  
Two Dimensional ◽  
First Passage ◽  
Explicit Representations ◽  
Mean Vectors ◽  
First Passage Problem

The process of interest is a controlled random walk in two dimensions: whenever the walker is above the main diagonal, the next increment to his position is chosen from a distribution FA ; whenever the walker is below the diagonal, the next increment comes from another distribution FB. The two distributions have mean vectors which tend to push the walker back toward the diagonal. We analyze the problem of first passage to the first quadrant, obtaining explicit representations for the limiting first-entry distribution and expected first-passage time.

scholarly journals Двумерные O(n)-модели с дефектами типа "случайная локальная анизотропия"

2020 ◽  
Vol 62 (4) ◽  
pp. 610
Author(s):  
А.А. Берзин ◽  
А.И. Морозов ◽  
А.С. Сигов
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Order Parameter ◽  
Easy Axis ◽  
Critical Value ◽  
Smooth Transition ◽  
Two Dimensional ◽  
Continuous Symmetry ◽  
Local Anisotropy ◽  
Ordered State

The phase diagram of two-dimensional systems with continuous symmetry of the vector order parameter containing defects of the “random local anisotropy” type is investigated. In the case of a weakly anisotropic distribution of the easy anisotropy axes in the space of the order parameter, with decreasing temperature, a smooth transition takes place from the paramagnetic phase with dynamic fluctuations of the order parameter to the Imri-Ma phase with its static fluctuations. In the case when the anisotropic distribution of the easy axes induces a global anisotropy of the “easy axis” type that exceeds a critical value, the system goes into the Ising class of universality, and a phase transition to the ordered state occurs in it at a finite temperature.

Duality of the Two-dimensional Ising Model

2020 ◽  
pp. 161-188
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Phase Transition ◽  
High Temperature ◽  
Ising Model ◽  
Statistical Models ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Duality Transformations ◽  
Peierls Argument ◽  
Chapter Deal ◽  
Sum Formula

Chapter 4 begins by discussing the Peierls argument, which allows us to prove the existence of a phase transition in the two-dimensional Ising model. The remaining sections of the chapter deal with duality transformations (duality in square, hexagonal and triangular lattices) that link the low- and high-temperature phases of several statistical models. Particularly important is the proof of the so-called star-triangle identity. This identity will be crucial in the later discussion of the transfer matrix of the Ising model. Finally, it covers the aspect of duality in two dimensions. An appendix provides information about the Poisson sum formula.

Temperature Effect on the Two-Dimensional Phase Transition Kinetics of Adenine Adsorbed at the Hg Electrode/Aqueous Solution Interface

2003 ◽  
Vol 68 (8) ◽  
pp. 1407-1419 ◽  
Author(s):  
Claudio Fontanesi ◽  
Roberto Andreoli ◽  
Luca Benedetti ◽  
Roberto Giovanardi ◽  
Paolo Ferrarini
Keyword(s):  
Phase Transition ◽  
Aqueous Solution ◽  
Phase Change ◽  
Temperature Effect ◽  
Transition Rate ◽  
Effect Of Temperature ◽  
Two Dimensional ◽  
Solution Interface ◽  
Phase Transition Kinetics ◽  
Kinetics Of

The kinetics of the liquid-like → solid-like 2D phase transition of adenine adsorbed at the Hg/aqueous solution interface is studied. Attention is focused on the effect of temperature on the rate of phase change; an increase in temperature is found to cause a decrease of transition rate.

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