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.
(J. Phys. Soc. Jpn., 92, 054003 (2023))
Monte Carlo simulations yielded examples of small spin clusters that exhibit a qualitative change in their character upon temperature variation. Headless spins on vertices of the regular octahedron (6 spins) and icositetrachoron (24 spins), a hyper polyhedron in dimension four, communicate with the neighbors through interaction that prefers mutual twists. The qualitative change arises from the twist interaction and the triangular "lattice" geometry, often tempting to bring frustration.
(J. Phys. Soc. Jpn., 91, 104603 (2022))
Numerical experiments on the Heisenberg model of headless spins, which prefer mutual twists, are performed for the two-dimensional triangular lattice under external fields to squeeze information of the phase transition proposed previously without field [J. Phys. Soc. Jpn., 90, 124003, (2021)], which brings only a local order below the transition temperature. A phase transition that accompanies a change in spatial periodicity occurs at practically the same temperature as without the field. The analyses of the field-effect reveal a hidden instability to the nematic order. The state diagram for a broad parameter range indicates that the temperature characteristic of the instability is appreciably higher than the phase transition temperature, implying a feeble effect of the field on the phase transition. Discussed are some specific properties of the model, such as macroscopic degeneracy of the ground state, the absence of frustration, spin order under the field, and phase transition exhibited by the continuous spin model in the two-dimension.
(J. Phys. Soc. Jpn., 91, 074007 (2022))
Numerical experiments on the Heisenberg model of headless spins are performed for the two-dimensional triangular lattice. The assumed model is with the two-body interaction preferring twisted alignment, which tends to exhibit sublattice order at the absolute zero. A possible phase transition is suggested based on prolonged Monte Carlo steps necessary for equilibration, a pronounced peak of heat capacity, and local violation of the sixfold symmetry inherent to the lattice. The entropy gain associated with the heat capacity peak implies that the transition accompanies the disordering over three spin orientations defined locally.
(J. Phys. Soc. Jpn., 90, 124003 (2021))