Abstract
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 inequalitydm2/dσ≦Z, where σ=m02 is a bare mass2 andZ is the strength of the particle pole, is basic to our method. This inequality implies inequalities for critical exponents.
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