Ground state of the spin-1/2 Heisenberg antiferromagnet on a two-dimensional square-hexagonal-dodecagonal lattice

TL;DR

This paper investigates the ground state magnetic order of a spin-1/2 Heisenberg antiferromagnet on a two-dimensional lattice composed of squares, hexagons, and dodecagons, demonstrating the presence of Neel long-range order.

Contribution

It introduces the study of Neel long-range order in a new uniform bipartite lattice with mixed polygons, expanding understanding of magnetic order in Archimedean lattices.

Findings

Neel long-range order is present in the studied lattice.

The study suggests a broader conjecture about NLRO in Archimedean lattices.

The work extends previous analyses to a new lattice type.

Abstract

Up to now, the existence of the the magnetic Neel Long Range Order (NLRO) in nearest neighbor, spin-1/2 antiferromagnetic (AF) lattice systems has been examined for seven, from the eleven existing, two-dimensional, uniform lattices. Plaquettes forming these uniform (Archimedean) lattices (e.g. square, triangular, kagome) are different regular polygons. An investigation of the NLRO in the ground state of AF spin systems on the seventh uniform (bipartite) lattice consisting of squares, hexagons and dodecagons is presented. The NLRO is shown to occur in this system. A simple conjecture concerning the existence of the NLRO in the ground state of antiferromagnetic, spin-1/2 systems on two dimensional, Archimedean lattices, is formulated.