| An important development in the theory of phase transitions was the understanding of how thermal fluctuations can alter the analytical properties of the free energy, modifying the critical exponents of a second-order phase transition. A second consequence, equally fundamental but less widely explored, is that thermal fluctuations can also change the order of the transition.; One specific mechanism for a fluctuation-induced first-order transition was proposed over two decades ago by Halperin, Lubensky and Ma (HLM). In this mechanism, the coupling between the fluctuations of a gauge field and the order parameter can convert a second-order transition into a first-order one. Such an effect is expected in two systems: in type-1 superconductors and the nematic-smectic-A (NA) transition. This effect is immeasurably small in superconductors; at the NA transition it is weak but detectable.; In this thesis, I explore the HLM effect at the NA transition experimentally. Because of the anisotropy of the nematic phase and the importance of both nematic and smectic fluctuations, this transition has remained an incompletely understood problem in condensed matter physics. The role of fluctuations is particularly interesting and complicated in the region of material-parameter space close to the Landau tricritical point (LTP), where the HLM effect is expected to be most pronounced.; I introduce a new high-resolution, real-space optical technique to probe the order of the NA transition. I have looked at the liquid crystal 8CB experimentally by measuring, using real-space imaging, the magnitude of nematic director fluctuations near TNA. Although the latent heat of 8CB is smaller than the resolution of the best adiabatic calorimeters, a well-resolved, discontinuous jump in the magnitude of the fluctuations is observed is observed on crossing the NA transition. This discontinuity is quantified by the dimensionless temperature t0.; Theoretically, on adding an external field to the HLM theory, one finds that a modest (magnetic) field of 10 T can drive the transition in 8CB back to second order. Moreover, the theory predicts a linear suppression of t0 for small fields, with a non-analytic cusp at H = 0. Using these results, one can test this non-analytic signature of the HLM theory in detail.; Looking for this effect experimentally, I find, surprisingly, no evidence for this effect at magnetic fields up to 1.5T, implying a critical field of >30 T. This and measurements in 8CB–10CB mixtures close to the LTP put bounds on the validity of the HLM theory, while at the same time confirming quantitatively the existence of a weakly first-order regime on the “second-order” side of the LTP. |
