Smectic A To C Phase Transition In Compressed Aerogel

We studied theoretically the smectic A to C phase transition in an anisotropic disordered environment. Such an environment can be prepared by absorbing the liquid crystal into a compressed aerogel with the compression along the smectic layers. Our theoretical approach is a classical theoretical field theory combined with renormalization group(?=7/2-d expansion) technique. Since our model is quite complicated, involving two field variables, we integrated out one of the variables to obtain an effective model only in terms of the other. Based on this effective model, we analyze the universality class of the phase transition. Our final conclusion is the following: 1) The disorder has a significant effect on the transition. In the absence of the disorder, the universality class of the transition belongs to “3D XY Model”. In the presence of the disorder, it becomes “3D Random Field Ising Model”. 2) The layer fluctuations have no effect on the critical behavior. This implies, even if the smectic layers are completely fixed by an external field assuming such an imaginary field exists, the universality class of this transition will remain the same. As we all know, the critical behavior of a phase transition is largely affected by fluctuations. The layer fluctuations in this problem are enormous due to the disorder; even so, they are negligible in determining the nature of the phase transition, which is quite a surprise.