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We calculate the dynamic phase transition (DPT) temperatures and present thedynamic phase diagrams in the Blume-Capel model under the presence of atime-dependent oscillating external magnetic field by using the pathprobability method. We study the time variation of the average order parametersto obtain the phases in the system and the paramagnetic (P), ferromagnetic (F)and the F + P mixed phases are found. We also investigate the thermal behaviorof the dynamic order parameters to analyze the nature (continuous anddiscontinuous) of transitions and to obtain the DPT points. We present thedynamic phase diagrams in three planes, namely (T, h), (d, T) and (k2/k1, T),where T is the reduced temperature, h the reduced magnetic field amplitude, dthe reduced crystal-field interaction and the k2, k1 rate constants. The phasediagrams exhibit dynamic tricritical and reentrant behaviors as well as adouble critical end point and triple point, strongly depending on the values ofthe interaction parameters and the rate constants. We compare and discuss thedynamic phase diagrams with dynamic phase diagrams that are obtained within theGlauber-type stochastic dynamics based on the mean-field theory and theeffective field theory.

Dynamic phase diagrams of the Blume-Capel model in an oscillating field by the path probability method