Distinguish empirical and crossover-theory descriptions of the critical-temperature shift

Determine whether the empirical power-law description or the renormalization-group crossover-theory description correctly characterizes the asymptotic dependence of the DBC model’s critical-temperature shift on the effective interaction range.

Background

The study compares the critical-temperature shifts of the degenerate blinking-checkers (DBC) model against both an empirical power law and a crossover-theory expression derived for three-dimensional Ising-like systems. The available simulations cover only a limited range of interaction lengths and shift magnitudes, and the largest interaction ranges may be affected by finite-size effects. Consequently, the reported data do not resolve which description governs the asymptotic regime; larger simulations may be needed to identify the predicted scaling.

References

Within the uncertainty of the simulation data, the limited range explored (approximately one decade in $\Delta\hat{T}\text{CP}$), and the possibility of finite-size effects in the system with the largest $r\text{eff}$ investigated, the present results do not allow a clear distinction between the empirical and theoretical descriptions.

— 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 3.2, paragraph “Critical Point Behavior”

Given the uncertainty of the MC density estimates ($\delta\rho\approx\pm0.01$), the available data are insufficient to establish either a universal functional dependence or the presence of exclusively logarithmic corrections.

— 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 3.2, paragraph following Fig. 4(e)

To the best of our knowledge, no theoretical description has been established for the dependence of the $\lambda$EP temperature or density on $r_\text{eff}$.

— 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 3.2, paragraph “Lambda End Point”