Metastability for Kawasaki dynamics on the hexagonal lattice

The paper defines the model, Hamiltonian H(η)=−U·(# interior bonds)+Δ·(# particles) with bonds counted only in Λ−, and Δ∈(U,3U/2) (reversible Metropolis Kawasaki with open boundary), then proves Xm={empty}, Xs={full} and Φ(empty,full)=ΓK-Hex, with ΓK-Hex given explicitly in two cases depending on δ, plus the e^{βΓK-Hex} time scale and limiting Exp(1) law. These appear in (2.3), Theorem 2.2 and Theorem 2.3, respectively . The “reference path” (upper bound) and the isoperimetric/perimeter-minimization lower bound (via quasi-regular hexagons with bars, EB5(r*) or EB1(r*+1)) yield the barrier (2.32) and gate description (Theorem 2.5) . The candidate solution’s decomposition H=Δ(|S|+|B|)−U·e(S) and 3|S|=2e(S)+p(S) matches the paper’s counting framework and VA-manifold stratification; their exact counting for rings reproduces the coefficients in (2.32), including the “+Δ traveler.” Their canonical (monotone) path and isoperimetric lower bound align with the paper’s Sections 3.2–3.3, and their δ-split gate geometry (five-side truncated ring versus two-segment overshoot) matches EB5(r*) and EB1(r*+1) with added triangles/free particle in Theorem 2.5 . Differences are present only in presentation: the paper characterizes a full gate family K(A*−1)fp, whereas the model summary highlights the two canonical prototypes; for the time law the paper proceeds via pathwise tools while the candidate cites potential-theoretic metastability. Substantively, both are consistent and correct.