Calculation of spin correlations in two-dimensional Ising systems from one-dimensional kinetic models

Kinetic spin models of the type first introduced by Glauber are considered with the most general choice of transition rates. It is shown that their time evolution operator can be related to the transfer matrices of certain two-dimensional Ising lattices. This allows an exact calculation of spin correlation functions at certain temperatures. Specifically we show that for the triangular antiferromagnet this special temperature corresponds to the disorder point. For the Hamiltonian version of the ANNNI model the corresponding result restricts in an important way the possible structure of the phase diagram.