Three-Step Ordering of Classical Headless Spins Preferring Twists on Icositetrachoric Honeycomb, a Four-Dimensional Analog of the Triangular Lattice

Abstract

Four-dimensional space-filling by regular icositetrachorons (24-cell) results in a rare example of highly symmetric tripartite lattices. Assuming the interaction preferring mutual twists, Monte Carlo simulations of classical headless spins on its sites yielded four phases: disordered, nematic (axially symmetric), threefold-symmetric, and biaxially disordered phases with decreasing temperature. The ordering behavior is discussed while comparing the behavior of the same model on the triangular lattice with/without external fields. The biaxial phase is compatible with the ground-state spin configurations with the absolute minimum of interaction without frustrations. The phase diagram covering a region of merely the nematic order is presented.