Goldstone modes and coexistence in isotropic N-vector models

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Abstract
Coexistence in the d-dimensional, isotropic, N-component phi 4 model is studied at first order in epsilon =4-d, using a renormalisation technique similar to that appropriate for bicritical crossover. The central result is the identification of a zero-temperature fixed point controlling the Goldstone singularities, with coupling constant u** varies as epsilon /(N-1)+O( epsilon 2), at which the transverse fields have canonical scaling dimensions. Both critical and Goldstone singularities are fully regularised by this renormalisation group, and a complete exponentiation of the equation of state is achieved. The leading behaviour of the correlation functions is also exhibited.