Qualitatively modifying twisted bilayer clock models with q>5

Investigate how to qualitatively modify the thermodynamic behavior of twisted bilayer q-state clock systems with q>5 by tuning additional system parameters.

Background

The paper reports that twisting produces qualitative thermodynamic anomalies for q=2–5, whereas bilayer clock systems with q>5 generally retain the qualitative behavior of their single-layer counterparts as the twist angle varies. The authors therefore identify the problem of finding additional parameter regimes or controls capable of inducing qualitative changes in the thermodynamic behavior of these higher-q systems as an unresolved direction for future study.

References

How to qualitatively modify the behavior of the $q>5$ bilayer systems, if desired, may require tuning additional system parameters---a direction that remains open for future study.

— Twist-controlled thermodynamic anomalies in bilayer q-state clock models  (2610.21949 - Yu et al., 15 Oct 2026) in Appendix, Section “q=4 and q=6 cases”