On phase transitions in the antiferromagnetic ising model

The diagram method is used to study the thermodynamic behavior of an Ising antiferromagnet with nearest-neighbor interaction as a function of the number of spatial dimensions $n$. In the diagram expansions of the thermodynamic quantities we separate out contributions that partly allow for the correlation energy, which is completely ignored in the selfconsistent-field approximation. If $n$ is finite, it is shown that the system is a single-phase state, but at large $n$ the asymptotic expansions of the thermodynamic quantities have singularities. In the limit $n\to\infty$ the adopted approximation leads to a phase transition described by the Curie–Weiss approximation, which, as is well known, becomes exact in this limit. The absence of a phase transition for finite $n$, predicted in the present approximation, is discussed.