Singularities induced by Goldstone modes

Abstract

We clarify and extend previous calculations of thermodynamic behavior of a system with a continuous symmetry, close to the coexistence curve (the region of small external field, below the critical temperature). The Goldstone modes induce singular terms, in, for example, the equation of state, whose coefficients may be evaluated in the $\ensuremath{\epsilon}$ expansion. The corrections of order $\ensuremath{\epsilon}$ to these critical amplitudes are large and suggest that these singularities may be observable. A discontinuity in three dimensions is noted in one amplitude.