Comparison of Heisenberg, two state Ising and 2 S + 1 state Ising model Hamiltonian on the magnetic and magneto-caloric properties of ferromagnetic systems

Abstract Monte Carlo simulations using the Metropolis algorithm were carried out for the Heisenberg model, the two-state Ising model, and the 2 S + 1 state Ising model, focusing on ferromagnetic systems. The relationship between magnetic exchange interaction strength and the ferromagnetic transition temperature ( T C ) was evaluated and compared across the three models within the range of 1 / 2 ⩽ S ⩽ 10 . Additionally, the magnetocaloric properties, such as the isothermal magnetic entropy change ( Δ S mag ) and the relative cooling power, were assessed for two well-known ferromagnetic materials: Gd and EuS. Among the three models examined, the 2 S + 1 state Ising model demonstrated the best quantitative agreement with experimental results, whereas the Heisenberg model showed poor agreement.