Dependence of Critical Temperature on Dispersion of Connections in 2D Grid

摘要

The calculation of probabilities in many problems of computer vision and machine learning is reduced to the finding of a normalizing constant (partition function). In the paper we evaluate the normalizing constant for a two-dimensional nearest-neighboring Ising model with almost constant average interaction between neighbors with a little noise. The two-dimensional Ising model is a perfect object for investigation. Firstly, a plane grid can be regarded as a set of image pixels. Secondly, the statistical physics offers an exact analytical solution obtained by Onsager for identical grid elements. We carry out numerical experiments to compute the normalizing constant for the case in which the noise in grid elements grows smoothly, analyze the results and compare them with Onsager's solution.