Goldstone mode singularities in specific heats and non-ordering susceptibilities of isotropic systems

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Abstract
Goldstone mode singularities in non-ordering correlation functions of the O(N)-symmetric phi 4 theory are investigated in 4- epsilon dimensions. Functions constructed from non-invariant combinations of the transverse operator pi 2 and the longitudinal operators sigma 2 and sigma generally exhibit severe infrared divergences on the coexistence curve. In low-order perturbative calculations of, for example, the specific heat, however, these divergences cancel. Such cancellations are shown to be a general feature of O(N)-symmetric correlation functions. Non-leading singularities remain, and lead to momentum dependence which can be expressed as a double power series in mod p mod epsilon and mod p mod 2- epsilon .