The McMillan-de Gennes Approach

McMillan [17] was the first to suggest that the N-SmA transition should in general be continuous. The smectic A phase is characterized by a density modulation in a direction z normal to the layers 

This situation is analogous to that of superfluid helium 4, where the order parameter is a wave function, leading to the now well known analogy between the N-SmA transition and the X point in He described by de Gennes and McMillan [18-20], 

Near the transition, the free energy can be expanded as a function of yr according to the relationship 

As a matter of fact, the N-SmA transition may be either second or first order. It becomes first order when a coupling exists between the smectic and the nematic ordering [17-21]. The orientational order parameter is S=Sn+6S, where 5 is the order pa- 

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