Physical realizations ofn≥4-component vector models. II.ε-expansion analysis of the critical behavior

Abstract

In the preceding paper, we derived $n\ge 4$-component Landau-Ginzburg-Wilson Hamiltonians describing phase transitions in certain physical systems. Here, we use Wilson's $\epsilon$ expansion to study the phase transitions associated with these Hamiltonians. Although the $n=4\mathrm{}$ systems Tb${\mathrm{Au}}_2$, Dy${\mathrm{C}}_2$, and Nb${\mathrm{O}}_2$ have different symmetries, they are predicted to have the same critical exponents. Similarly, although the $n=6\mathrm{}$ systems Tb${\mathrm{D}}_2$, Nd, and ${\mathrm{K}}_2$Ir${\mathrm{Cl}}_6$ have different symmetries, their critical exponents are predicted to be equal, but different from those of an isotropic $n=6\mathrm{}$ model. We suggest these predictions be tested experimentally. Three of the Hamiltonians we have considered possess no stable fixed points. Two of the materials U${\mathrm{O}}_2$ ($n=6\mathrm{}$) and MnO ($n=9\mathrm{}$) described by these Hamiltonians are known to have first-order transitions. We suggest that experiments should be performed to test whether or not the transitions in the $n=8\mathrm{}$ systems ErSb, MnSe, NiO, and in the $n=4\mathrm{}$ systems TbAs, TbP, TbSb are first order.