Critical exponents and elementary particles

Particles are shown to exist for a.e. value of the mass in single phase φ⁴ lattice and continuum field theories and nearest neighbor Ising models. The particles occur in the form of poles at imaginary (Minkowski) momenta of the Fourier transformed two point function. The new inequality dm²/dσ≦Z, where σ=m₀² is a bare mass² and Z is the strength of the particle pole, is basic to our method. This inequality implies inequalities for critical exponents.