Generalized Schottky anomaly

The Schottky anomaly in the specific heat is one of the most universal phenomena in nature. The generalized Schottky anomaly for the combined system of two Hamiltonians ℋ_1 = - μ B∑_i σ _i ( B : magnetic field) and ℋ_2 = - J∑_⟨i,j⟩σ _i σ _j ( J : coupling constant), both showing the Schottky anomaly, is systematically investigated for the first time. For a small magnetic field, we find the new fact that the maximum of the Schottky anomaly increases sharply and the Schottky temperature falls and then rises (making a sharp v shape) as the magnetic field B is increased. For a large magnetic field, as B increases, the maximum of the Schottky anomaly decreases, and the Schottky temperature increases gradually, in agreement with recent experimental measurements.