Effect of order parameter fluctuations on the Halperin-Lubensky-Ma first-order transition in superconductors and liquid crystals

Abstract

We show that order-parameter fluctuations in a good type-I superconductor or a liquid crystal always increase the size of the first-order transition. This behavior is eventually changed when the system crosses over to inverted-XY critical behavior, with the size of the first-order transition vanishing as a power law with a crossover exponent. We find good agreement between our theory and a recent experiment on the nematic-smectic-A first-order transition in 8CB-10CB mixtures of liquid crystals.More than 25 years ago, Halperin, Lubensky and Ma (HLM) [1] and Coleman and Weinberg [2] demonstrated that when a scalar field is coupled to a gauge field, the fluctuations of the gauge field can change the nature of the phase transition in the theory from continuous to first order. The coupling of a scalar field (or an order parameter (OP)) to a massless gauge field arises often in physics: the Meissner transition in superconductors [3], the Higgs mechanism in particle physics [4], and the nematic-smectic-A transition in liquid crystals [5] are among the best-known examples [6], [7]. The analysis of HLM initially centered on the fluctuations of the gauge field and neglected the OP fluctuations, which is justifiable for good type-I superconductors (with Ginzburg-Landau parameter κ ≪ 1), where the size (to be precisely defined shortly) of the first-order transition is larger. This approximation, however, inevitably breaks down for strong type-II materials (κ ≫ 1), where neglecting the OP fluctuations would yield a first-order transition well into the critical region. Close to four dimensions, the effect of the OP fluctuations can be studied using the Wilson-Fisher renormalization group [1], which, however, in this case leads only to "run-away" flows and no stable critical points. This is usually interpreted as a sign of a first-order transition [1], [8]. Today, based on accumulated analytical and numerical evidence, it is generally believed that the transition for κ ≫ 1 is again second order, in the so-called inverted-XY universality class [9][10][11][12][13][14][15][16]. The corresponding topology of the flow of the coupling constants under scaling transformation is depicted in Fig. 1. It may thus seem natural to expect that the OP fluctuations should decrease the size of the first-order transition, finally reducing it to zero at the crossover to inverted-XY critical behavior.The fluctuation effects in question are unfortunately too fine to be observable even in high-T c superconductors on account of the smallness of the fine-structure constant [17,18]. But in liquid crystals, the coupling of the smectic OP to the director fluctuations is stronger, and the fluctuations at the nematic-smectic-A transition become an issue of central importance. A recent experiment on twocomponent liquid-crystal mixtures [19] found a surprising result: the size of the first-order transition is larger than the prediction of the HLM theory. Motivated by this result, in this Letter we consider theoretically the effect of OP fluctuations on the ...

Nature of the Quantum Phase Transition to a Spin-Nematic Phase

“…Another possibility is that the transition remains second order, but the coupling to the additional soft modes changes the universality class. This is believed to be the case deep in the type-II region [16,17].…”

“…For κ > 0, and especially for κ >> 1 (type-II limit), the role of OP fluctuations must be examined. This is a difficult problem that has been studied for classical transitions [16,17], and to some extent for the quantum s-wave ferromagnetic one [32], but more work is needed on magnetic transitions in this limit. Fourth, all of our conclusions also hold for spin nematics in higher angular momentum channels, only the realization of the conjugate field changes.…”