Potts models and the critical behavior of a cubic ferromagnet with fourth- and sixth-order anisotropy

Abstract

The critical behavior of the magnetization of a cubic ferromagnet in a magnetic field is analyzed for all field directions when both fourth- and sixth-order anisotropy are present. Results are presented for ${K}_{1}g0$ and all $\ensuremath{\kappa} (\frac{{K}_{2}}{{K}_{1}})$. For $\ensuremath{-}6l\ensuremath{\kappa}l9$ the phase diagram is of the three-state Potts type. For $\ensuremath{\kappa}g9$ a 60\ifmmode^\circ\else\textdegree\fi{} rotation of the three-state Potts diagram is obtained at high fields and a reentrant feature at lower fields. For $\ensuremath{\kappa}=9$, a special critical point appears on the [111] axis. The connection between this result and an extended version of the Landau theory is made. Finally, the $\ensuremath{\kappa}\ensuremath{\le}\ensuremath{-}6$ ([110] hard) diagram is displayed and the nature of the critical points, lines, and surfaces discussed.