Monte Carlo study of the classical antiferromagnetic $J_1$-$J_2$-$J_3$ Heisenberg model on a simple cubic lattice

A. N. Ignatenko; S. V. Streltsov; V. Yu. Irkhin

doi:10.1134/S0031918X2560277X

paper

Monte Carlo study of the classical antiferromagnetic $J_{1}$ - $J_{2}$ - $J_{3}$ Heisenberg model on a simple cubic lattice

arXiv:2602.16471 · doi:10.1134/S0031918X2560277X

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 $J_{2} / J_{1}$ , $J_{3} / J_{1}$ ratios, and temperature. The character of the phase transitions is analyzed via the Binder cumulant method. The Neel temperature $T_{N}$ and the frustration parameter (the ratio $f = ∣ θ ∣/ T_{N}$ , $θ$ 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 CaMnO $_{3}$ and HgMnO $_{3}$ , are discussed.

8 pages, 11 figures, 36 references

Monte Carlo study of the classical antiferromagnetic J1​-J2​-J3​ Heisenberg model on a simple cubic lattice

Abstract

Monte Carlo study of the classical antiferromagnetic $J_{1}$ - $J_{2}$ - $J_{3}$ Heisenberg model on a simple cubic lattice