Topology of space of periodic ground states in antiferromagnetic Ising and Potts models in selected spatial structures

TL;DR

This paper investigates the topology of the space of periodic ground states in antiferromagnetic Ising and Potts models across various lattices, revealing conditions under which these states form connected or isolated graphs.

Contribution

It introduces a novel analysis of the ground state space topology in specific lattice structures, highlighting cases with connected state graphs.

Findings

Most ground states are isolated nodes in the state space.

Connected graphs occur in certain systems, allowing zero-energy magnetization changes.

Ground states are classified by degree and neighbor types.

Abstract

Topology of the space of periodic ground states in the antiferromagnetic Ising and Potts (3-state) models is analysed in selected spatial structures. The states are treated as graph nodes, connected by one-spin-flip transitions. The spatial structures are the triangular lattice, the Archimedean ($3,12^{2}$) lattice and the cubic Laves C15 lattice with the periodic boundary conditions. In most cases the ground states are isolated nodes, but for selected systems we obtain connected graphs. The latter means that the magnetisation can vary in time with zero energy cost. The ground states are classified according to their degree and type of neighbours.