True critical behaviour of the nematic to smectic-A transition · revision history

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Accepted · first revision · record

Title

True critical behaviour of the nematic to smectic-A transition

Plain

When a nematic liquid crystal forms layers it becomes a smectic-A, and this transition was predicted to behave like the superconducting transition. Measured critical exponents instead vary from material to material and differ along and across the layers, and the true behaviour has not been settled for about fifty years.

Precise

For the N to SmA transition in thermotropic liquid crystals (e.g. 8CB), the de Gennes analogy predicts 3D XY exponents ($\alpha$ near -0.015, $\nu$ near 0.67), while Halperin-Lubensky-Ma theory predicts that director fluctuations drive a weakly first-order transition and dual analyses suggest inverted-XY scaling. Experiments find effective exponents $\alpha$, $\nu_{\mathrm{par}}$, $\nu_{\mathrm{perp}}$ that vary with the nematic range $T_{\mathrm{NA}}/T_{\mathrm{NI}}$ and show $\nu_{\mathrm{par}}$ larger than $\nu_{\mathrm{perp}}$. Determine the asymptotic critical behaviour: first order, isotropic inverted-XY, or a distinct anisotropic fixed point, with the crossover length.

Settled by

High-resolution calorimetry and X-ray correlation-length measurements closer to $T_{\mathrm{NA}}$ than currently reached, combined with large-scale simulation or renormalization-group analysis of the coupled director and smectic fields.

Kind

well-posed

Answer type

classification

References

(empty)

Literature status

open

Status note

The nonuniversal exponents were reviewed in 1994 (Garland and Nounesis, Phys. Rev. E, https://doi.org/10.1103/PhysRevE.49.2964); no resolution found in the arXiv record through 2026.

Posed since

1972