Election opinion dynamics through the 2D Ising model
The Ising model and its variations have seen regular applications in describing the behavior of systems with many interacting bodies of varying complexity. We explored a zero-field Ising model that includes next nearest neighbor interactions with strength J2 to investigate the opinion dynamics of a voting population in a two-party election. We constructed lattices filled with voters preferring to vote for either x candidate or x' candidate in random configurations. We then allowed these sites to switch preferences using the Metropolis algorithm while varying the influence strength J2, of the "clique" of each voter. Our work demonstrates that, when exposing the voting population to biased information/disinformation, increasing J2 leads to a decrease in the critical bias of the voters where the overall "alignment" of their voting preferences drops to zero. We also investigated how this introduction of next nearest neighbor interactions is affected by changes in voting population size. Here, we found out that the rate of change at which the critical bias decreases is reduced as the population becomes larger due to the sheer amount of voters inhibiting long-range order among them.