Abstract
An extensive Monte Carlo study of the classical Heisenberg model on a simple cubic lattice with antiferromagnetic exchange interactions \({{J}_{n}}\) between the first, second, and third neighbors is performed in a broad region of \({{{{J}_{2}}} \mathord{\left/ {\vphantom {{{{J}_{2}}} {{{J}_{1}}}}} \right. \kern-0em} {{{J}_{1}}}}\) , \({{{{J}_{3}}} \mathord{\left/ {\vphantom {{{{J}_{3}}} {{{J}_{1}}}}} \right. \kern-0em} {{{J}_{1}}}}\) ratios, and temperature. The character of the phase transitions is analyzed via the Binder cumulant method. The Néel temperature \({{T}_{{\text{N}}}}\) and the frustration parameter (the ratio \(f = {{\left| \theta \right|} \mathord{\left/ {\vphantom {{\left| \theta \right|} {{{T}_{{\text{N}}}}}}} \right. \kern-0em} {{{T}_{{\text{N}}}}}}\) , \(\theta \) being the Curie–Weiss temperature) are calculated. A comparison with the Tyablikov approximation is carried out. The strength of the frustration effects is explored. Possible applications to antiferromagnetic perovskites, such as CaMnO3 and HgMnO3, are discussed.
