Critical exponents for phi3-field models with long-range interactions.

The critical exponents for two φ3-field theories with long-range (LR) interactions decaying as 1/Rd+σ, σ>0, are calculated to two-loop order in renormalized perturbation theory in d=3σ-e’ dimensions. One is the continuum version of the p-state Potts model and the other is the scalar field theory with imaginary coupling that describes the Yang-Lee edge-singularity problem. The two crossover exponents for quadratic symmetry breaking discussed by Wallace and Young and in recent work by the present authors are also calculated in the first case. By means of renormalization-group recursion relations to one-loop order, it is shown that the LR fixed point is stable for all σ 2)-state Potts model there is an indication of a continuous crossover to SR behavior at σ=2-ηSR, with ηSR>0. It is pointed out that a number of exact results [β=(1-e’/2σ)σν, σ^=(d-σ)/(d+σ), in which σ^ is the Yang-Lee edge-singularity exponent, and ν−1=(d-σ)/2 for a scalar theory] may apply within the LR expansion depending on η=2-σ (shown here to hold at least to two-loop order) being exact, to all orders.