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We derive probabilistic limit theorems that reveal the intricate structure of the phase transitions in a mean-field version of the Blume-Emery-Griffiths model. These probabilistic limit theorems consist of scaling limits for the total spin and moderate deviation principles (MDPs) for the total spin. The model under study is defined by a probability distribution that depends on the parameters
Of all the scaling limits, the structure of those near the tricritical point is by far the most complex, exhibiting new types of critical behavior when observed in a limit-theorem phase diagram in the space of the two parameters that parametrize the scaling limits. The scaling limits and the MDPs are derived via a unified method based on two components: analyzing the Taylor expansions of a function