Violation of the Conformal Limit at Finite Density: Insights from Effective Models and Lattice QCD

In this work, we discuss recent results obtained with the application of the medium separation scheme (MSS) in different contexts where a clear violation of the conformal limit for the speed of sound at finite density has been observed in Quantum Chromodynamics (QCD). We analyze several scenarios, including QCD at finite isospin density, two-color QCD, and two-flavor color superconductivity. Whenever possible, we compare our findings with lattice QCD (LQCD) results, showing that the Nambu--Jona-Lasinio (NJL) model combined with the MSS provides a consistent description across different regimes of the QCD phase diagram. Our analysis highlights how effective models, when properly regularized, can capture essential nonperturbative features of dense QCD matter, offering complementary insights to lattice simulations.