Tuning stripe-phase domains via five-coordinated vertex arrangement in the SEH_00 Ising model

Determine whether the sizes and orientations of stripe-phase spin domains in the antiferromagnetic nearest- and next-nearest-neighbor Ising model with J1 = J2 = -1 on the SEH_00 single-edge-length hexagonal quasiperiodic tiling can be controlled by modifying the spatial arrangement of the five-coordinated vertices (coordination number 5) inherent to this tiling’s vertex set, which arise from its ordered vacancy defects relative to a triangular lattice.

Background

In the paper, Monte Carlo simulations of the J1–J2 Ising model were performed on three structures: a perfect triangular lattice, a triangular lattice with randomly positioned vacancy defects, and the SEH_00 tiling whose vertices can be viewed as a triangular lattice decorated by a quasiperiodically ordered set of vacancy defects. For J1 = J2 = -1 (both antiferromagnetic), the triangular lattice exhibits a stripe-ordered phase, while the SEH_00 and defect lattices show reduced long-range order and multiple coexisting stripe orientations.

The authors identify five-coordinated vertices as crucial local environments affecting stripe orientation because these sites experience strong constraints from six next-nearest neighbors. They pose the open question of whether adjusting the spatial distribution of such five-coordinated vertices could systematically tune stripe domain sizes or orientations in the SEH_00 tiling (and related defect lattices).