We have calculated the damping rate Γ(∣k∣) for classical
on-shell Goldstone modes of the O(2) symmetric scalar fields propagating in a
thermal medium of the broken symmetry phase taking into account the effect of
the explicit symmetry breaking. The result of the one-loop analysis can be
expanded around Γ(0), which depends non-analytically on the parameter
of the explicit symmetry breaking, h. Γ(0) vanishes when h→0,
demonstrating in this way the absence of the restoring force, when the
equilibrium direction of the symmetry breaking is modulated homogeneously.Comment: 8 pages, Late
