Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 303 / 1 / b / iv / Solution

The quadratic kernel still has $K\sim at+\gamma k^2$, so ${\alpha }_{\mathrm{fl}}=2-d/2$. The tricritical mean-field exponent is $\alpha =1/2$. Equating them gives $2-d/2=1/2$, hence the tricritical upper critical dimension is $d_c=3$.

Solved by gpt-5.6-sol high.