Exact Results for Two-Dimensional Ising Models

1999 ◽  
pp. 205-240
Author(s):  
David A. Lavis ◽  
George M. Bell
Keyword(s):  
Ising Models ◽  
Exact Results ◽  
Two Dimensional

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.

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.

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

Mott-Hubbard transition in finite one- and two-dimensional lattices: Exact results

1997 ◽  
Vol 230-232 ◽  
pp. 1031-1033 ◽  
Author(s):  
A.N. Kocharian ◽  
A.K. Jermakian ◽  
A. Sogomonian
Keyword(s):  
Exact Results ◽  
Two Dimensional

scholarly journals Surface Critical Behavior of Two-Dimensional Dilute Ising Models

1997 ◽  
Vol 89 (5-6) ◽  
pp. 1079-1085 ◽  
Author(s):  
W. Selke ◽  
F. Szalma ◽  
P. Lajkó ◽  
F. Iglói
Keyword(s):  
Critical Behavior ◽  
Ising Models ◽  
Two Dimensional ◽  
Surface Critical Behavior

Exact results in the two-dimensional U(1)-symmetric Thirring model

1984 ◽  
Vol 230 (4) ◽  
pp. 511-547 ◽  
Author(s):  
G.I. Japaridze ◽  
A.A. Nersesyan ◽  
P.B. Wiegmann
Keyword(s):  
Thirring Model ◽  
Exact Results ◽  
Two Dimensional
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