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.

scholarly journals Дальний порядок в двумерных O(n)-моделях, индуцированный случайными полями, и состояние Имри-Ма

2020 ◽  
Vol 62 (2) ◽  
pp. 281
Author(s):  
А.А. Берзин ◽  
А.И. Морозов ◽  
А.С. Сигов
Keyword(s):  
Phase Transition ◽  
Local Field ◽  
Random Fields ◽  
Order Parameter ◽  
Smooth Transition ◽  
Two Dimensional ◽  
Strong Anisotropy ◽  
Continuous Symmetry ◽  
Weak Anisotropy ◽  
Ordered State

A.A. Berzin, A.I. Morosov, and A.S. Sigov The influence of defects of the “random local field” type with an anisotropic distribution of random fields on two-dimensional models with continuous symmetry of the vector order parameter is considered. In the case of weak anisotropy of random fields, with decreasing temperature there takes place a smooth transition from the paramagnetic phase with dynamic fluctuations of the order parameter to the Imry-Ma phase with static fluctuations caused by fluctuations of the random field of defects. In the case of strong anisotropy of random fields, defects lead to an effective decrease in the number of components of the order parameter and the appearance of a phase transition to an ordered state at finite temperature.

The flattening phase transition in systems of trapped ions

2009 ◽  
Vol 87 (10) ◽  
pp. 1425-1435 ◽  
Author(s):  
Taunia L. L. Closson ◽  
Marc R. Roussel
Keyword(s):  
Phase Transition ◽  
Critical Exponent ◽  
Order Parameter ◽  
Ion Trap ◽  
Anisotropy Parameter ◽  
Critical Value ◽  
Trapped Ions ◽  
Dimensional Structure ◽  
Flattening Process ◽  
Second Order Phase Transition

When the anisotropy of a harmonic ion trap is increased, the ions eventually collapse into a two-dimensional structure consisting of concentric shells of ions. This collapse generally behaves like a second-order phase transition. A graph of the critical value of the anisotropy parameter vs. the number of ions displays substructure closely related to the inner-shell configurations of the clusters. The critical exponent for the order parameter of this phase transition (maximum extent in the z direction) was found computationally to have the value β = 1/2. A second critical exponent related to displacements perpendicular to the z axis was found to have the value δ = 1. Using these estimates of the critical exponents, we derive an equation that relates the amplitudes of the displacements of the ions parallel to the x–y plane to the amplitudes along the z axis during the flattening process.

Formation of Periodic Ripples in a Surface Skin

1977 ◽  
Vol 32 (1) ◽  
pp. 33-39
Author(s):  
Fred Fischer
Keyword(s):  
Phase Transition ◽  
Order Parameter ◽  
Liquid Surface ◽  
Compressive Strain ◽  
Critical Value ◽  
Skin Thickness ◽  
Skin Area ◽  
Ripple Formation ◽  
Elastic Skin ◽  
Second Order Phase Transition

Abstract A solid elastic skin on a liquid surface aquires a periodic ripple formation when a compressive strain surpasses a critical value. From a calculation the ripple wavelength is found to be proportional to the 3/4th power of the skin thickness. This instability can be described as a kind of second order phase transition, where a relative amplitude of the ripple wave is the order parameter. In addition, when the skin area is abruptly compressed the ripple wavelength depends on the magnitude of the compressive strain. Examples for skin rippling with wavelengths between 10 μm and 100 m are discussed.

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 the random triangle model

1999 ◽  
Vol 36 (04) ◽  
pp. 1101-1115 ◽  
Author(s):  
Olle Häggström ◽  
Johan Jonasson
Keyword(s):  
Phase Transition ◽  
Social Networks ◽  
Ising Model ◽  
Hexagonal Lattice ◽  
Graph Model ◽  
Finite Graph ◽  
Critical Value ◽  
Two Dimensional ◽  
Random Graph Model ◽  
Image Position

The random triangle model was recently introduced as a random graph model that captures the property of transitivity that is often found in social networks, i.e. the property that given that two vertices are second neighbors, they are more likely to be neighbors. For parameters p ∊ [0,1] and q ≥ 1, and a finite graph G = (V, E), it assigns to elements η of {0,1} E probabilities which are proportional to where t(η) is the number of triangles in the open subgraph. In this paper the behavior of the random triangle model on the two-dimensional triangular lattice is studied. By mapping the system onto an Ising model with external field on the hexagonal lattice, it is shown that phase transition occurs if and only if p = (q−1)−2/3 and q > q c for a critical value q c which turns out to equal It is furthermore demonstrated that phase transition cannot occur unless p = p c (q), the critical value for percolation of open edges for given q. This implies that for q ≥ q c , p c (q) = (q−1)−2/3.

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.

SIX-VERTEX MODELS AS FERMI GASES

1991 ◽  
Vol 05 (14) ◽  
pp. 2385-2400
Author(s):  
PETER ORLAND
Keyword(s):  
Phase Diagram ◽  
Free Energy ◽  
Order Parameter ◽  
Fermi Gases ◽  
Two Dimensional ◽  
Vertex Model ◽  
Energy Correlation ◽  
Free Fermions ◽  
Parameter Correlation ◽  
Simple Physical Interpretation

The two-dimensional six-vertex model with a particular choice of external field is known to be equivalent to a theory of free Fermions. Two conditions are made on the six-vertex weights. A simple physical interpretation of the ordered and disordered phases is found. The Fermi sea is filled and the free energy, correlation length, order parameter, correlation functions and phase diagram are determined.

LOCAL MINIMIZERS FOR THE GINZBURG–LANDAU ENERGY NEAR CRITICAL MAGNETIC FIELD: PART I

1999 ◽  
Vol 01 (02) ◽  
pp. 213-254 ◽  
Author(s):  
SYLVIA SERFATY
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
Critical Value ◽  
Critical Magnetic Field ◽  
Two Dimensional ◽  
Local Minimizers ◽  
Large Parameter ◽  
Ginzburg Landau

We find local minimizers of the two-dimensional Ginzburg–Landau functionals depending on a large parameter κ, which describe the behavior of a superconductor in a prescribed exterior magnetic field hex. We prove an estimate on the critical value Hc1 of hex(κ), corresponding to the first phase-transition in which vortices appear in the superconductor; and we locate these vortices.

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.

ROUGHNESS INFLUENCE ON SURFACE MELTING

2001 ◽  
Vol 08 (06) ◽  
pp. 599-608 ◽  
Author(s):  
FRAY DE LANDA CASTILLO ALVARADO ◽  
MARGARITO CRUZ PINEDA ◽  
JERZY H. RUTKOWSKI ◽  
LESZEK WOJTCZAK
Keyword(s):  
Field Theory ◽  
Phase Transition ◽  
Phase Diagram ◽  
Order Parameter ◽  
Surface Melting ◽  
Density Fluctuations ◽  
Solid Model ◽  
Van Der Waals Equation ◽  
Liquid Phases ◽  
Two Phases

The influence of surface roughness on surface melting phase transition is discussed within the molecular field theory. The roughness is characterized by the surface order parameter averaged over all the density fluctuations whose description corresponds to the discrete Gaussian solid-on-solid model. The potential governing the transition between the rough surface and the surface melting is considered in terms of the modified van der Waals equation of state. Its effective shape represents two intersecting parabolas with nonequal curvatures for the solid and liquid phases. The phase diagram shows the coexistence of two phases with rough and wet surfaces.

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