Scale-dependence of Elastic Constants in the Decoupled Lamellar Phase of Tethered Crystalline Membranes

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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 Lamé coefficients, and the cross-coupling elastic constant vanish as (q)⁻ ᵃ whereas the bend elastic constant diverges as (q)ᵇ, with a, b > 0, as the wavenumber q tends to zero. The exponents a and b satisfy the relation a + 3b = 2.