Correlation function for a plane Ising lattice

R. Z. Bariev, M.P. Zhelifonov

G. V. Ryazanov

Rainer J. Jelitto

R Badke, V. Rittenberg, H. Ruegg

Using conformal invariance one can derive the correlation functions on a disc from those in the half-plane. The correlation function in the half-plane is determined by the 'small' conformal invariance up to an unknown function of one variable. By measuring, using the Monte Carlo method, the correlation function for two different configurations, the unknown function can be eliminated and one obtains a test of conformal invariance. It is shown that the Ising and the three-state Potts model pass the test for very small lattices.

Antoine Georges, David Hansel, Pierre Le Doussal +1 more

The exact calculation of an infinite number of correlation functions for general cubic and HCP anisotropic Ising models on their 'disorder variety' is described. The intra-plane correlation functions are found to be exactly the same as for a two-dimensional free-fermion Ising model. This allows the authors to characterise the intersection between the disorder and critical variety which displays in general anisotropic scaling with non-trivial exponents.

C. Ruge, P. Zhu, F. Wagner