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We investigate the thermodynamic properties of the zero-field Blume-Capelmodel in the vicinity of its tricritical point (TCP). We calculate thequadrupole moment, internal energy, and entropy densities employing an exactnumerical recursion procedure for the model defined on a hierarchical latticeof fractal dimension $d$. We explore the scaling behavior of the isothermalquadrupolar susceptibility and, the isothermal and constant crystal-fieldspecific heat as a function of the temperature and the reduced crystal-fieldparameter along the ferromagnetic and the \emph{ordered paramagnetic} phasefrontier. Results achieved for systems with dimensions $d=2$ and $3$ exhibitthe main features of the continuous and first-order transitions in the TCPneighborhoods. We also probe the phase coexistence in the $\lambda$-diagram andthe latent heat in the vicinity of the tricritical point locus.

Thermodynamical behavior of the Blume-Capel model in the vicinity of its tricritical point