Physical realizations ofn≥4-component vector models. I. Derivation of the Landau-Ginzburg-Wilson Hamiltonians

Abstract

Certain phase transitions which involve an increase of the unit cell in one or more directions, are described by $n\ge 4$-component vector models. According to universality, the critical behavior of a system should depend only upon a small number of parameters such as the dimensionality of space, the number of components of the order parameter, and the symmetry of the Hamiltonian. We suggest that it would be of great interest to study these $n\ge 4$ systems experimentally, and examine the effect of the dimensionality of the order parameter and the anisotropy of the system on the critical behavior. We use the group-theoretical method of landau and Lifshitz to derive the Landau-Ginzburg-Wilson Hamiltonians corresponding to the following $n\ge 4$ systems: type-II antiferromagnets TbAs, TbP, TbSb ($n=4\mathrm{}$), and MnO, MnSe, NiO, and ErSb ($n=8\mathrm{}$); type-I antiferromagnet U${\mathrm{O}}_2$ ($n=6\mathrm{}$); type-III antiferromagnet ${\mathrm{K}}_2$Ir${\mathrm{Cl}}_6$ ($n=6\mathrm{}$); sinusoidal magnetic systems Dy${\mathrm{C}}_2$ and Tb${\mathrm{Au}}_2$ ($n=4\mathrm{}$), and Tb${\mathrm{D}}_2$ and Nd ($n=6\mathrm{}$); and an $n=4\mathrm{}$ system, Nb${\mathrm{O}}_2$, which exhibits a structural transition. In the following paper (II) we use the exact renormalization-group technique in $d=4-\epsilon$ dimensions to study the critical behavior of these Hamiltonians.