Abstract:
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.