Highly macroscopically degenerated single-point ground states as source of specific heat capacity anomalies in magnetic frustrated systems

Highlights: • Exact investigation of specific heat in a frustrated magnetic system is performed. • Residual entropies of all ground states are found. • Source of the specific heat anomalies in frustrated magnetic systems is identified. • Field-induced double-peak structure of specific heat in frustrated systems is predicted. Anomalies of the specific heat capacity are investigated in the framework of the exactly solvable antiferromagnetic spin-$1/2$ Ising model in the external magnetic field on the geometrically frustrated tetrahedron recursive lattice. It is shown that the Schottky-type anomaly in the behavior of the specific heat capacity is related to the existence of unique highly macroscopically degenerated single-point ground states which are formed on the borders between neighboring plateau-like ground states. It is also shown that the very existence of these single-point ground states with large residual entropies predicts the appearance of another anomaly in the behavior of the specific heat capacity for low temperatures, namely, the field-induced double-peak structure, which exists, and should be observed experimentally, along with the Schottky-type anomaly in various frustrated magnetic system.