The Halperin-Lubensky-Ma argument on the nature of the liquid-crystalline nematic-to-smectic A phase transition: what we have learnt from experiments over the past 50 years

The nematic-to-smectic A (N-SmA) is one of the most extensively studied phase transitions in the field of liquid crystals and, beyond any doubt, the most controversial one. Half a century ago, Halperin, Lubensky and Ma (HLM), based on the analogies between Type-I superconductors and liquid crystals, predicted that the N-SmA transition should always be (at least weakly) first-order. The entropy discontinuity, recognised as scant and challenging to detect in the case of large nematic ranges, arises from a coupling between the nematic director fluctuations and the smectic order parameter. In this review, we briefly refer to the development of various theoretical approaches to explain the nature of this phase transition starting from the early 1970s, with a primary emphasis on the placement of the HLM argument. Following that, we comprehensively review the experiments conducted from that point onwards to characterise the critical behaviour of the N-SmA transition and specifically to detect this discontinuity, providing experimental evidence on the HLM argument.