The Schottky-type specific heat as an indicator of relative degeneracy between ground and first-excited states: the case study of regular Ising polyhedra

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The specific heat of regular Ising polyhedra is investigated in detail as a function of temperature and magnetic field. It is shown that the regular Ising polyhedra display diverse double-peak temperature dependences of the specific heat whenever the magnetic field approaches a level-crossing field. The Schottky theory of a two-level system often provides a plausible explanation of a height and position of low-temperature peak, which emerges in the specific heat of a regular Ising polyhedron due to low-lying excitations from a ground state to a first-excited state. The height and position of Schottky-type maximum depends essentially on a relative degeneracy of the ground state and first-excited state, which are in general quite distinct in geometrically frustrated Ising spin clusters. Low-temperature variations of the specific heat with the magnetic field exhibit multipeak structure with two peaks (of generally different height) symmetrically placed around each level-crossing field.