Correlations at the nematic to smectic-A critical point when ν ∥ = 2ν⊥

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Abstract
We express the physical order parameter for the nematic to smectic-A (NA) transition in terms of an order parameter in another gauge where phase fluctuations are a minimum. We show that when ν∥ = 2 ν⟩ in three dimensions, the physical order parameter correlation function G(x) shows power law decay in x for reduced temperature t ≤ 0. The exponents η∥ (t = 0) and η⟩ (t = 0) describing this decay are not equal to lim η∥ (t) and lim η⟩(t) respectively. This result is in agreement with recent conjectures by Nelson and Toner