On the critical cluster in the two-dimensional Ising model: Computer-assisted exact results

2004 ◽  
Vol 121 (22) ◽  
pp. 11232 ◽  
Author(s):  
Vitaly A. Shneidman ◽  
Gelu M. Nita
Keyword(s):  
Ising Model ◽  
Computer Assisted ◽  
Exact Results ◽  
Two Dimensional ◽  
Critical Cluster ◽  
Model Computer

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 Magnetization Profile in the D= 2 Semi-Infinite Ising Model and Crossover Between Ordinary and Normal Transition

1997 ◽  
Vol 11 (17) ◽  
pp. 2075-2091 ◽  
Author(s):  
Peter Czerner ◽  
Uwe Ritschel
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
Short Distance ◽  
Higher Dimensions ◽  
Scaling Analysis ◽  
Exact Results ◽  
Two Dimensional ◽  
Normal Transition ◽  
Surface Magnetization ◽  
Logarithmic Dependence

We study the two-dimensional semi-infinite Ising model with a free surface at or near bulk criticality. Special attention is paid to the influence of a boundary magnetic field h1 on the surface-near regime and the crossover between the fixed points at h1=0 and h1=∞. Near the surface, a smallh1 causes a steeply increasing magnetization m(z)~z3/8 log z as the distance z increases away from the surface. By means of a phenomenological scaling analysis, this phenomenon can be related to the well-known logarithmic dependence of the surface magnetization m1 on h1. Our analysis provides a deeper understanding of the existing exact results on m(z) and relates the short-distance phenomena in d=2 to those in higher dimensions. Both the results of the scaling analysis and the exact analytic profiles are corroborated by Monte Carlo simulations.

Two-dimensional Ising model in an annealed random field: Exact results

1986 ◽  
Vol 33 (7) ◽  
pp. 4762-4766 ◽  
Author(s):  
L. L. Gonçalves ◽  
R. B. Stinchcombe
Keyword(s):  
Ising Model ◽  
Random Field ◽  
Exact Results ◽  
Two Dimensional

Computer Assisted Image Reconstruction of Oligomer Structure

1976 ◽  
Vol 34 ◽  
pp. 472-473
Author(s):  
A.M. Jones ◽  
A. Max Fiskin
Keyword(s):  
Three Dimensional ◽  
Depth Of Field ◽  
Computer Assisted ◽  
Projection Data ◽  
Two Dimensional ◽  
Single Particles ◽  
Dimensional Reconstruction ◽  
Computer Assisted Image ◽  
The Fourier Transform ◽  
Space Approach

If the tilt of a specimen can be varied either by the strategy of observing identical particles orientated randomly or by use of a eucentric goniometer stage, three dimensional reconstruction procedures are available (l). If the specimens, such as small protein aggregates, lack periodicity, direct space methods compete favorably in ease of implementation with reconstruction by the Fourier (transform) space approach (2). Regardless of method, reconstruction is possible because useful specimen thicknesses are always much less than the depth of field in an electron microscope. Thus electron images record the amount of stain in columns of the object normal to the recording plates. For single particles, practical considerations dictate that the specimen be tilted precisely about a single axis. In so doing a reconstructed image is achieved serially from two-dimensional sections which in turn are generated by a series of back-to-front lines of projection data.

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