Spin correlations in the Ising chains

Combining the Greenʹs function method with the transfer matrix technique, the three-site spin correlations in the one-chain and two-chain Ising lattices are studied exactly. The results show that although the magnetizations of the Ising chains vanish when the external magnetic field is zero, the spins are strongly correlated in these chains. The dependence of the spin correlations of the two-chain on the inter-chain interaction indicates that the inter-chain interaction has significant effect on the spin correlations but there does not exist a dimensional crossover from the one-dimensional model to the two-dimensional one.