Skeleton inequalities and mean field properties for lattice spin systems

We present a proof of skeleton inequalities for ferromagnetic lattice spin systems with potential V(φ²) = (a/2)φ² + Σ_{n = 2}^M {λ_2n/(2n)!} φ²ⁿ (a real, λ_2n ≥0) generalizing the Brydges-Fröhlich-Sokal and Bovier-Felder methods. As an application of the inequalities, we prove that, for sufficiently soft systems in d > 4 dimensions, critical exponents γ, α, and Δ₄ take their mean-field values (i.e., γ = 1, α = 0, and Δ₄ = 3/2).