= Solution
A <tricritical point> requires two independent even coefficients in the <Landau free energy> to vanish: $r=u=0$, with $v>0$ providing stability. At $h=0$, the ordinary critical line $r=0,u>0$ meets the <tricritical three-phase line> $r=3u^2/(16v),u<0$. The <order parameter> discontinuity along the first-order line is $\sqrt{-3u/(4v)}$, which goes to zero at their meeting.
The positive sextic coefficient makes this a different leading local potential from an ordinary quartic <critical point>. Consequently its <mean-field critical exponents>, crossover behavior and <upper critical dimension> differ. There are two relevant even tuning directions near the <tricritical point>, in addition to the conjugate odd field. The root solution and labelled <phase diagram> display the three controls and the <tricritical wings>; varying $h$ can give a first-order reversal within the ordered coexistence sheet, a first-order weak/strong transition on a wing, or a continuous transition at a wing's ordinary critical edge.
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