We investigate a simple Landau—Ginzburg field theory for the contrarian voter Ising model proposed by Devauchelle et al. [Phys. Rev. E 109, 044106 (2024)], with the aim of explaining the occurrence of tight margin of victories in apparently most nationwide binary election results nowadays. We focus on proving rigorously, at the level of the simplified field theory, one of the numerically found features of the original model, namely, that binary elections tend to have small margin of victories in large enough countries, a finding that is consistent with existing data [op. cit.]. The question translates to an interesting problem in the calculus of variations in our case, which we attempt to answer. This talk presents the partial results and the difficulties yet to be overcome.
Link to the above mentioned paper https://arxiv.org/abs/2402.12207