On the Asymptotic Behaviour of the Mayer Cluster Series in the Antiferromagnetic Problem

In continuation of the work of a former paper, it is shown that the Mayer series for the antiferromagnetic problem can be related in various ways to the placing of links on the lattice. The two such transformations found in the former paper are shown to be special cases of a general theory, which can also be used to relate many other problems of physical interest with the Onsager-Ising problem. The Mayer series is analysed into sub-series, the behaviour of some of which can be determined from known results on the `link' problem, while that of others can, in principle, be obtained from the general transformation theory just mentioned. The conclusion of the former paper, that the Mayer z-series has a positive singularity determining the transition but a negative singularity nearer the origin determining its radius of convergence, is confirmed, as are most of the conclusions from the earlier work. The results appear to be reliable in the interesting region near T = 0 but break down as we approach H = 0 on the transition curve.