Magnetic field-induced degenerate ground state in the classical antiferromagnetic XX model on the icosahedron

Abstract The ground state of the classical antiferromagnetic XX model in a magnetic field is calculated for spins mounted on the vertices of the icosahedron. The magnetization is characterized by two discontinuities as a function of the external field. For a wide field range above the first discontinuity the ground state is degenerate, with two spins related by spatial inversion almost aligned with the field and the rest forming two magnetization units in the form of pentagons. It is shown that the degeneracy originates from the coupling of the two pentagons, which introduces the triangle, associated with ground-state degeneracy, as an interaction unit in the icosahedron. The magnetization discontinuities are shown to evolve first from the coupling of isolated triangles and then from the addition of the two spins related by spatial inversion.