  Specific heat measurements constitute one of the most powerful experimental
methods to probe fundamental excitations in solids. After the proposition of
Einstein's model, more than one century ago (Annalen der Physik \textbf{22},
180 (1907)), several theoretical models have been proposed to describe
experimental results. Here we report on a detailed analysis of the two-peak
specific heat anomalies observed in several materials. Employing a simple
multilevel model, varying the spacing between the energy levels $\Delta_i$ =
$(E_i$ $-$ $E_{0})$ and the degeneracy of each energy level $g_i$, we derive
the required conditions for the appearance of such anomalies. Our findings
indicate that a ratio of $\Delta_2$/$\Delta_1$ $\thickapprox$ 10 between the
energy levels and a high degeneracy of one of the energy levels define the
two-peaks regime in the specific heat. Our approach accurately matches recent
experimental results. Furthermore, using a mean-field approach we calculate the
specific heat of a degenerate Schottky-like system undergoing a ferromagnetic
(FM) phase transition. Our results reveal that as the degeneracy is increased
the Schottky maximum in the specific heat becomes narrow while the peak
associated with the FM transition remains unaffected.
