The estimates of correlations in two-dimensional Ising model

We investigate the correlation inequalities and the decay of correlations of stochastic Ising model in a rectangle with side length 2L×K(LlnL)1/2, where K is some positive constant. With different boundary conditions, at inverse temperature β>βc or β<βc and zero external field, we show some estimates of the correlation functions for the two-dimensional Ising model.