φ24 quantum field model in the single-phase region: Differentiability of the mass and bounds on critical exponents

We prove that the physical mass m is a differentiable function of the bare mass m₀ down to the critical point (defined by the occurrence of m=0 or of the onset of symmetry breaking). We derive an upper bound on m'(m₀). We show that the critical exponents η, ν, γ, ζ are bounded from below by their classical values.