Entropic independence for ferromagnetic two-spin systems below λ_c

Determine whether the entropic independence condition (in the sense of Anari–Jain–Koehler–Pham–Vuong, 2022) holds for (β,γ,λ)-ferromagnetic two-spin systems on general graphs with β ≤ 1 < γ, βγ > 1, and λ < λ_c(β,γ) := (γ/β)^{sqrt(βγ)/(sqrt(βγ) − 1)}.

Background

The authors suggest that refined mixing-time boosting techniques could potentially yield near-optimal Glauber dynamics mixing times, but those techniques require verifying entropic independence, a stronger property than spectral independence.

Whether entropic independence holds for the ferromagnetic two-spin systems considered here (with λ below λ_c) is currently unknown, and resolving this would enable the use of sharper boosting frameworks to improve mixing bounds.