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We consider the phase diagram of a ferromagnetic system driven to a quantumphase transition with a tuning parameter $p$. Before being suppressed, thetransition becomes of the first order at a tricritical point, from which wingsemerge under application of the magnetic field $H$ in the $T$-$p$-$H$ phasediagram. We show that the edge of the wings merge with tangent slopes at thetricritical point.

Constraints on the merging of the transition lines at the tricritical point in a wing-structure phase diagram