Geodesic
On phase transitions in the antiferromagnetic ising model
Teoretičeskaâ i matematičeskaâ fizika, Tome 13 (1972) no. 2, pp. 276-285

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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. 
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     author = {V. Ya. Krivnov and B. N. Provotorov and M. E. Sarychev},
     title = {On phase transitions in the antiferromagnetic ising model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {276--285},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1972_13_2_a10/}
}
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V. Ya. Krivnov; B. N. Provotorov; M. E. Sarychev. On phase transitions in the antiferromagnetic ising model. Teoretičeskaâ i matematičeskaâ fizika, Tome 13 (1972) no. 2, pp. 276-285. http://geodesic.mathdoc.fr/item/TMF_1972_13_2_a10/