Harvest cycle decision making as modelled by statistical physics - Nyu, Clovis Qi Long (Nanyang Technological University, 2021)
The Ising model, and other spin models, are conceptual paradigms often used by statistical Physicists to study magnetic systems. They are employed to demonstrate order-disorder phase transitions by vary ing key parameters. In this report, long range non-decaying anti-ferromagnetic interactions are added to the standard ferromagnetic Ising model to study the decision making process of farmers deciding on their harvest cycles. Through the analytical technique of Mean Field Theory, and numerical simulations based on the Metropolis-Hastings algorithm, phase transitions have been confirmed for various combinations of parameters. Phase diagrams of the Magnetization show agreement between the theoretical work and the simulations. At a critical inverse temperature beta, there exists an order-disorder transition which has an inverse linear dependence on the strength of both the ferromagnetic and anti-ferromagnetic interactions. Additionally, there exists a single cluster-double cluster transition within the ordered phase which is charac terised by a linear relation between the ferromagnetic and anti-ferromagnetic interactions. Additionally, the simulations seem to indicate a smooth transition from the disordered state to the double cluster state. Aside from this, it was found that the anti-ferromagnetic interactions have a limited effect on the internal energy of the system, as compared to the ferromagnetic interactions. Finally, it was also found that the presence of a weak external magnetic field can bias a lattice in the single cluster state towards a specific orientation. However, a much stronger external field must be present to overcome the thermal fluctuations, when the lattice is in the disordered state, and the anti-ferromagnetic interactions, when the lattice is in the double cluster state.