Scale-dependence of Elastic Constants in the Decoupled Lamellar Phase of   Tethered Crystalline Membranes
  We analyse the effect of thermal fluctuations on the elastic constants of the decoupled lamellar phase of tethered, crystalline membranes. Using a momentum-shell renormalization group technique, we show that the smectic-A -like compressional elastic constant, the in-plane Lam\'{e} coefficients, and the cross-coupling elastic constant vanish as (\ln q)^{- a} whereas the bend elastic constant diverges as (\ln q)^{b}, with a, b > 0, as the wavenumber q tends to zero. The exponents a and b satisfy the relation a + 3b = 2. 
Yashodhan Hatwalne and Sriram Ramaswamy