  We consider the 3-state Potts model in $d\geq2$ dimensions. For $d$ less than
the upper critical dimension $d_\text{crit}$, the model has a critical and a
tricritical fixed point. In $d=2$, these fixed points are described by minimal
models, and so are exactly solvable. For $d>2$, however, strong coupling makes
them difficult to study and there is no consensus on the value of
$d_\text{crit}$. We use the numerical conformal bootstrap to compute critical
exponents of both the critical and tricritical fixed points for general $d$. In
$d=2$ our results match the expected values, and as we increase $d$ we find
that the critical exponents of each fixed point get closer until they merge
near $d_\text{crit}\lesssim 2.5$.
