Complex-Temperature Phase Diagrams of 1D Spin Models with Next-Nearest-Neighbor Couplings

TL;DR

This paper investigates how adding next-nearest-neighbor couplings affects the complex-temperature phase diagrams of 1D spin models, using exactly solvable models like the Ising and Potts models.

Contribution

It provides exact phase diagrams for 1D Ising and Potts models with both nearest and next-nearest-neighbor couplings, highlighting the impact of these couplings on phase behavior.

Findings

Exact phase diagrams for various J_nnn/J_nn ratios

Comparison between models with and without NNN couplings

Insights into the role of NNN interactions in phase structure

Abstract

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 1D Ising model with nearest-neighbor (NN) and next-to-nearest-neighbor (NNN) couplings. We work out the exact phase diagrams for various values of $J_{nnn}/J_{nn}$ and compare these with the case of pure nearest-neighbor (NN) couplings. We also give some similar results for the 1D Potts model with NN and NNN couplings.