Spontaneous symmetry breaking thermodynamic limit

To investigate spontaneous symmetry breaking, one ordinarily has to start at finite volume and insert a source which explicitly breaks the symmetry. The source is removed only after the infinite volume limit is taken. We stress that the source does not have to be a quark mass (it could be a higher dimension operator), so one can investigate symmetry breaking even when the quark mass is exactly zero throughout the calculation. (To be precise, a quark mass does not explicitly violate vector symmetries, so it cannot play the role of the source in the thermodynamic limit needed here.)... 

S ii(q = 0) describes the critical scattering along the coexistence curve, while Scoii(q = 0) describes the critical scattering for T > Tc and A i = 0 (i.e., at critical composition < > = crit). This fact that for the description of the response function, different expressions need to be used above and below the phase transition, in order to take into account the spontaneous symmetry breaking that appears in the thermodynamic limit between the coexisting phases, is well known [105] but has not been considered in some of the work on polymer mixtures [101-103, 107]. 

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