The antiferromagnetic Ising model on the swedenborgite lattice

TL;DR

This study investigates the antiferromagnetic Ising model on the three-dimensional swedenborgite lattice, revealing complex ground state degeneracies and phase transitions influenced by magnetic fields and coupling strengths.

Contribution

It provides the first explicit calculation of the ground state degeneracy and phase diagram of the Ising model on the swedenborgite lattice, including effects of magnetic fields.

Findings

Identified two distinct ground state manifolds with a first order transition at zero field.

Mapped the phase diagram showing degenerate and non-degenerate phases depending on field and coupling.

Calculated the residual entropy explicitly for the ground states.

Abstract

Geometrical frustration in spin systems often results in a large number of degenerate ground states. In this work we study the antiferromagnetic Ising model on the three dimensional swedenborgite lattice which is a specific stacking of Kagom\'e and triangular layers. The model contains two exchange couplings, one within the Kagom\'e layer, another one in between Kagom\'e and triangular layers. We determine the phase diagram with and without easy axis magnetic field and calculate the ground state degeneracy explicitly in terms of the residual entropy. At zero field we find two different ground state manifolds separated by a first order transition at T = 0 and equal exchange couplings. We also determine the T = 0 phase diagram in a magnetic field and find a rich phase diagram with both degenerate and non-degenerate phases depending on the field strength and out-of-plane coupling.