Renormalization-group analysis of metamagnetic tricritical behavior

A renormalization-group treatment of the tricitical behaviour of a $d$-dimensional metamagnet in a magnetic field is presented. For small $\epsilon =4-d>\mathrm{}0\mathrm{}$, the tricritical behavior is described by competitions between pairs of Gaussian-like and Ising-like fixed points. Despite the increased number of independent interacting fields, we find that the metamagnetic tricritical exponents maintain their classical values for $d>\mathrm{}3\mathrm{}$, with logarithmic corrections in three dimensions. The conclusions thus agree with those of Riedel and Wegner for an intrinsically simpler model appropriate to ${\mathrm{He}}^3$-${\mathrm{He}}^4$ mixtures. The effect of an ordering field is analyzed, and Ising exponents are found on the "wings" of the tricritical point.