We study the dependence of complex-temperature phase diagrams on details of the Hamiltonian, focusing on the effect of non-nearest-neighbor spin-spin couplings. For this purpose, we consider a simple exactly solvable model, the one-dimensional (1D) Ising model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) couplings. We work out the exact phase diagrams for various values of ${\mathrm{J}}_{\mathrm{NNN}}$/${\mathrm{J}}_{\mathrm{NN}}$ and compare these with the case of pure NN couplings. We also give some similar results for the 1D Potts model with NN and NNN couplings.

DOI:https://doi.org/10.1103/PhysRevE.55.5184