RIGOROUS INEQUALITY FOR THE SPECIFIC-HEAT OF AN ISING OR PHI-4 FERROMAGNET

For a class of models including the Ising ferromagnet and the φ4lattice field theory, I prove a rigorous upper bound for the specific heat in terms of the susceptibility and the magnetization. This bound implies the critical-exponent inequalities α ≤ max (0,( 2 - d 2)γ), α′ ≤ max (0,( 2 - d 2)γ′, γ′ - 2β), and αc ≤ max (0, ( 2 - d 2) (δ - 1), δ - 3) for lattice dimension d ≥ 2. © 1979.