In spontanious symmetry breaking we minimize lagrangian of zero temperature. These lagrangians are phenomenological lagrangians like Landau or Gizburg-landau or something like mean field. After we found a minimum we expand the previous lagrangian around one of the minima (optional(spontanious symmetry breaking)) we get to "mass term" for one field and we see that some field lost their mass. These massless particles play a great role in conveying long range order or collective mode.
Some of the well-known massless particles are phonons in superfluid He-4 and Magnons in magnetism or 3-D ising model. People call them Goldstone modes ( collective behavior(primary excitations) caused by waving of massless particles).
All in all, we have two mechanisms of symmetry breaking in physics. One is Goldstone mechanism and the second is Higgs mechanism. First one for short range forces like between two spin : $\sum_{ij}J S_i\cdot S_j$, and second kind longe range forces : $$\sum_{ij}\frac{e^2}{(r_i-r_j)^2}.$$
