Tricriticality in Crossed Ising Chains
Abstract
We explore the phase diagram of Ising spins on one-dimensional chains which criss-cross in two perpendicular directions and which are connected by interchain couplings. This system is of interest as a simpler, classical analog of a quantum Hamiltonian which has been proposed as a model of magnetic behavior in NbO and also, conceptually, as a geometry which is intermediate between one and two dimensions. Using mean field theory as well as Metropolis Monte Carlo and Wang-Landau simulations, we locate quantitatively the boundaries of four ordered phases. Each becomes an effective Ising model with unique effective couplings at large interchain coupling. Away from this limit we demonstrate non-trivial critical behavior, including tricritical points which separate first and second order phase transitions. Finally, we present evidence that this model belongs to the 2D Ising universality class.
Cite
@article{arxiv.1608.02974,
title = {Tricriticality in Crossed Ising Chains},
author = {T. Cary and R. R. P. Singh and R. T. Scalettar},
journal= {arXiv preprint arXiv:1608.02974},
year = {2017}
}