Resolve the nature of the shortest-range Type IV transition

Characterize whether the $Z_n=6$, $\bar{\omega}=5$ system possesses a genuine tricritical point, a closely separated critical point and lambda end point, or a coincident critical point and lambda end point producing confluent critical behavior.

Background

For the Type IV parameter choice ωˉ=5\bar{\omega}=5, systems with coordination numbers other than six display both a liquid–gas critical point and a distinct lambda end point. At Zn=6Z_n=6, however, the simulations do not resolve a separate lambda end point and instead appear consistent with a single tricritical point. The uncertainty in the simulation data leaves several possible interpretations, which could be distinguished by measuring second-order thermodynamic quantities such as susceptibility or correlation length.

References

The uncertainty in the simulation data may limit our ability to distinguish between a genuine TCP, a scenario in which a CP and $\lambda$-EP occur in extremely close proximity, and a scenario where the CP and $\lambda$-EP overlap at a single point, producing a confluence of critical behavior.

— Effects of Interaction Range on Fluid Multicriticality: A Computational Study of an Interconverting Lattice Model  (2609.09074 - Longo et al., 8 Sep 2026) in Section 3.1, paragraph discussing lattice effects