Crossover between field theories with short-range and long-range exchange or correlations

The relation between scalar field theories with short-range and long-range exchange or correlations is studied. It is shown to all orders in perturbation theory that the critical exponents of fields and composite operators are continuous functions of the parameters alpha ( xi ) characterising the decay rate of the long-range exchange (correlations) with power-like falloff 1/rd+2-2 alpha (1/rd-2 xi ). The scaling law (d-2 xi )v=2, where v is the correlation length exponent, as well as the Harris criteria (1970) are shown to be exact to all orders in perturbation theory. A discrepancy between two widely used approaches to the crossover problem is pointed out.