Metastability in tricritical systems

We present a Langer-Cahn-Hilliard-like theory of some aspects of nucleation for two tricritical systems: the symmetric scalar metamagnet and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixtures. In particular, we calculate the work of formation for a tricritical droplet and the imaginary part of the free energy associated with the metastable state. In addition we obtain an explicit expression for the interface tension whose critical exponent agrees with earlier phenomenological predictions. We find that the scaling form for the work of formation exhibits a universality with respect to critical and tricritical points. In addition, we find that the singularity on the coexistence curve for the metamagnet and on the superfluid side of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is of the same functional form as for Ising-like systems. However, the singularity is different on the normal side of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ coexistence curve, due to the role of the phase variable of the complex superfluid order parameter.