Abstract
The authors study scalar field theories for which the interaction term of the Hamiltonian is cubic in the fields. They indicate the circumstances for which field theory models of this type represent continuous phase transitions. The renormalisation group functions for these models are presented up to, and including, three-loop contributions, giving critical exponents to order epsilon 3 in 6- epsilon dimensions. The exponent sigma which characterises the Yang-Lee edge singularity is given explicitly to this order.
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