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We derive rates of convergence for limit theorems that reveal the intricatestructure of the phase transitions in a mean-field version of theBlume-Emery-Griffith model. The theorems consist of scaling limits for thetotal spin. The model depends on the inverse temperature $\beta$ and theinteraction strength $K$. The rates of convergence results are obtained as$(\beta,K)$ converges along appropriate sequences $(\beta_n,K_n)$ to pointsbelonging to various subsets of the phase diagram which include a curve ofsecond-order points and a tricritical point. We apply Stein's method for normaland non-normal approximation avoiding the use of transforms and supplyingbounds, such as those of Berry-Esseen quality, on approximation error. Weobserve an additional phase transition phenomenon in the sense that dependingon how fast $K_n$ and $\beta_n$ are converging to points in various subsets ofthe phase diagram, different rates of convergences to one and the same limitingdistribution occur.

Phase transitions for rates of convergence in the Blume-Emery-Griffiths model