Boundary Critical Behaviour of Two-Dimensional Layered Ising Models

1997 ◽  
Vol 11 (11) ◽  
pp. 1363-1388
Author(s):  
Alessandro Pelizzola
Keyword(s):  
Free Surface ◽  
Order Parameter ◽  
Ising Models ◽  
Coupling Constants ◽  
Critical Behaviour ◽  
Exact Results ◽  
Two Dimensional ◽  
Spatial Coordinate ◽  
Layered Models

Layered models are models in which the coupling constants depend in an arbitrary way on one spatial coordinate, usually the distance from a free surface or boundary. Here the theory of the boundary critical behaviour of two-dimensional layered Ising models, including the Hilhorst–van Leeuwen model and models for aperiodic systems, is reviewed, with a particular attention to exact results for the critical behaviour and the boundary order parameter.

ISING MODELS ON TWO-DIMENSIONAL QUASI-CRYSTALS: SOME EXACT RESULTS

1988 ◽  
Vol 02 (01) ◽  
pp. 49-63 ◽  
Author(s):  
T. C. CHOY
Keyword(s):  
Ising Model ◽  
Critical Exponents ◽  
Ising Models ◽  
Critical Surface ◽  
Exact Results ◽  
Two Dimensional ◽  
Soluble Model ◽  
De Bruijn ◽  
Quasi Crystals ◽  
Conventional Picture

Exactly soluble Z-invariant (or Baxter) models of statistical mechanics are generalised on two-dimensional Penrose lattices based on the de Bruijn construction. A unique soluble model is obtained for each realization of the Penrose lattice. Analysis of these models shows that they are soluble along a line in parameter space which intersects the critical surface at a point that can be determined exactly. In the Ising case, critical exponents along this line are identical with the regular two-dimensional Ising model thus supporting the conventional picture of the universality hypothesis.

scholarly journals Boundary critical behaviour of two-dimensional random Ising models

1998 ◽  
Vol 31 (12) ◽  
pp. 2801-2814 ◽  
Author(s):  
F Iglói ◽  
P Lajkó ◽  
W Selke ◽  
F Szalma
Keyword(s):  
Ising Models ◽  
Critical Behaviour ◽  
Two Dimensional

Differential Form of Real-Space Renormalization: Exact Results for Two-Dimensional Ising Models

1978 ◽  
Vol 40 (25) ◽  
pp. 1605-1608 ◽  
Author(s):  
H. J. Hilhorst ◽  
M. Schick ◽  
J. M. J. van Leeuwen
Keyword(s):  
Differential Form ◽  
Ising Models ◽  
Real Space ◽  
Exact Results ◽  
Two Dimensional

Erratum - Frustration in periodic systems : exact results for some 2D ising models

1979 ◽  
Vol 40 (10) ◽  
pp. 1024-1024
Author(s):  
G. André ◽  
R. Bidaux ◽  
J.-P. Carton ◽  
R. Conte ◽  
L. de Seze
Keyword(s):  
Ising Models ◽  
Periodic Systems ◽  
Exact Results

scholarly journals Universality class of the motility-induced critical point in large scale off-lattice simulations of active particles.

Soft Matter ◽  
2021 ◽  
Author(s):  
Claudio Maggi ◽  
Matteo Paoluzzi ◽  
Andrea Crisanti ◽  
Emanuela Zaccarelli ◽  
Nicoletta Gnan
Keyword(s):  
Phase Separation ◽  
Critical Point ◽  
Computer Simulations ◽  
Large Scale ◽  
Universality Class ◽  
Critical Behaviour ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Active Particles ◽  
Two Dimensional Model

We perform large-scale computer simulations of an off-lattice two-dimensional model of active particles undergoing a motility-induced phase separation (MIPS) to investigate the systems critical behaviour close to the critical point...

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

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