Conformal invariance and surface defects in the two-dimensional Ising model. Exact results

1990 ◽  
Vol 60 (1-2) ◽  
pp. 167-180
Author(s):  
Bertrand Berche ◽  
Lo�c Turban
Keyword(s):  
Ising Model ◽  
Conformal Invariance ◽  
Surface Defects ◽  
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.

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.

Sign in / Sign up

Export Citation Format

Share Document