We have calculated the damping rate Gamma(|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.
