Agreement of Capillary-Wave Theory with Exact Results for the Interface Profile of the Two-Dimensional Ising Model

1982 ◽  
Vol 48 (5) ◽  
pp. 368-368 ◽  
Author(s):  
Matthew P. A. Fisher ◽  
Daniel S. Fisher ◽  
John D. Weeks
Keyword(s):  
Ising Model ◽  
Capillary Wave ◽  
Wave Theory ◽  
Exact Results ◽  
Two Dimensional ◽  
Interface Profile

Thermal fluctuations in the interface of an inhomogeneous fluid

1982 ◽  
Vol 60 (2) ◽  
pp. 137-153 ◽  
Author(s):  
Luis de Sobrino ◽  
Jože Peternelj
Keyword(s):  
Capillary Wave ◽  
Mean Field Theory ◽  
Mean Field ◽  
Wave Theory ◽  
Thermal Fluctuations ◽  
Van Der Waals Gas ◽  
Inhomogeneous Fluid ◽  
Consistent Manner ◽  
The Mean ◽  
Interface Profile

We use van Kampen's expression for the partition function of a van der Waals gas to investigate the effect of noncritical fluctuations on the interface of an inhomogeneous fluid. Such a procedure combines in a consistent manner the results of mean field theory and of capillary wave theory and, in addition, uncovers contributions due to fluctuations of the interface profile. Although the latter add negligibly to the interfacial width, they result in corrections to the mean field surface tension comparable to those resulting from capillary fluctuations. The effect of the walls in limiting the fluctuations is explicitly taken into account.

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
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