Start with a simple scalar field Lagrangian L(ϕ) at zero temperature T=0, which has a hidden symmetry and spontaneously break it. By the standard procedure a field ϕ is redefined
ϕ→⟨ϕ⟩+ϕ′,
where ϕ′ is a quantum fluctuation around some constant value ⟨ϕ⟩. The constant value ⟨ϕ⟩ is called a condensate (or vacuum expectation value) of the field ϕ. (For example, in the case of pions and sigma mesons (L is a linear sigma model Lagrangian) fluctuations ϕ′ are physical pions and sigma mesons, with pion condensate equal to zero, and sigma meson condensate equal to ⟨σ⟩=fπ.)
The spontaneus symmetry breaking looks the same for T≠0 scalar field theory. Again, we redefine the field ϕ→⟨ϕ⟩+ϕ′ and obtain physical particles ϕ′ as a fluctuations around the condensate, which is now temperature dependent variable; and it can serve as an order parameter of the theory. (For example, in the case of sigma mesons and pions, the condensate ⟨σ⟩ will vanish at the chiral temperature point, displaying the existance of the chiral phase transition.)
So my question is, are the quantum fluctuations ϕ′ (i.e. the physical particles) the same in T=0 and T≠0 field theory? Or are they somehow 'mixed', so they are both thermal and quantum fluctuations? In addition, the diagram here http://upload.wikimedia.org/wikipedia/commons/0/06/QuantumPhaseTransition.png basically says that quantum and classical (critical) behaviour is the same thing, which adds up to my confusion.
Of course, if I completely missed the point, I hope that someone can explain in a better way what is the concept of the symmetry breaking and emergence of a condensate (and physical particles).
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