By Przytycki F., Urbanski M.
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Additional info for Conformal fractals, dimensions and ergodic theory
The Helfrich scenario can thus be relevant in certain materials. To date, however, there is no direct evidence of this continuous transition mechanism (the transition would be of order ∞ in the Ehrenfest classification). One way of answering this question was suggested by Holyst and Oswald  and consists in measuring the variation in the N-SmA transition temperature ( TNA ) in free-standing films as a function of their thickness H. Indeed, TNA must increase when the film gets thinner, but following very different laws depending on the type of the transition.
17) This formula shows that the latent heat must increase linearly with the concentration above the TCP. The prediction is not verified experimentally, at least close to the TCP, where it should be the most accurate (Fig. 6). 7 Fig. 6 Latent heat for the 8CB-10CB mixture as a function of the molar concentration in 10CB (from ref. ). This finding prompts us completely to revise the theoretical approach to the transition. 5 that the coupling with the director fluctuations, which we ignored so far, must be taken into account for a correct interpretation of the latent heat data close to the TCP.
32 STRUCTURE OF THE SMECTIC A PHASE AND THE TRANSITION TOWARD THE NEMATIC PHASE As a matter of fact, the cybotactic groups are elastically deformed when the field lines of the director are distorted. 16). More energy is then needed to distort the nematic. Let us determine the order of magnitude of this excess energy using the Landau-Ginzburg-de Gennes theory; one can easily see of eq. n and to determine the average of |Ψ|2 at this scale. This yields, using eq. 48) αξ3 Replacing in eq. 50b) ~ This important formula shows that the correction δK to the Frank constant K diverges with the correlation length at the transition.
Conformal fractals, dimensions and ergodic theory by Przytycki F., Urbanski M.