Abstract: We construct the tricritical point for a model of $n$-component continuous spins with $\phi^6$ interaction on the 3-dimensional integer lattice. We do the same for a supersymmetric version of the model, where the tricritical point is the so-called theta point for polymer collapse. In both cases, we prove that the tricritical two-point function has Gaussian decay, namely $|x|^{-1}$. The proof uses a rigorous renormalisation group analysis. This is joint work with Roland Bauerschmidt and Martin Lohmann.