Critical phenomena in the mean-field Ising model with five-spin coupling and magnetic field

Abstract This study investigates the critical properties of the mean-field Ising model incorporating five-spin interactions and external magnetic field. By using a variational approach to minimize free energy, the behaviour of the magnetic order parameter is systematically analysed across different phases. The research establishes the conditions for phase transitions, identifies critical points, and calculates the associated critical exponents. The model demonstrates unique phase behaviours, including the coexistence of thermodynamic equilibria and smooth transitions in magnetization. These results offer valuable insights into the impact of higher-order spin interactions in magnetic systems, with implications for understanding complex multi-spin dynamics in physical and biological networks.