TY - JOUR

T1 - Structure of physical crystalline membranes within the self-consistent screening approximation

AU - Gazit, Doron

PY - 2009/10/15

Y1 - 2009/10/15

N2 - The anomalous exponents governing the long-wavelength behavior of the flat phase of physical crystalline membranes are calculated within a self-consistent screening approximation (SCSA) applied to second order expansion in 1/ dC (dC is the codimension), extending the seminal work of Le Doussal and Radzihovsky [Phys. Rev. Lett. 69, 1209 (1992)]. In particular, the bending rigidity is found to harden algebraically in the long-wavelength limit with an exponent η=0.789..., which is used to extract the elasticity softening exponent ηu =0.422..., and the roughness exponent ζ=0.605.... The scaling relation ηu =2-2η is proven to hold to all orders in SCSA. Further, applying the SCSA to an expansion in 1/ dC, is found to be essential, as no solution to the self-consistent equations is found in a two-bubble level, which is the naive second-order expansion. Surprisingly, even though the expansion parameter for physical membrane is 1/ dC =1, the SCSA applied to second-order expansion deviates only slightly from the first order, increasing ζ by mere 0.016. This supports the high quality of the SCSA for physical crystalline membranes, as well as improves the comparison to experiments and numerical simulations of these systems. The prediction of SCSA applied to first order expansion for the Poisson ratio is shown to be exact to all orders.

AB - The anomalous exponents governing the long-wavelength behavior of the flat phase of physical crystalline membranes are calculated within a self-consistent screening approximation (SCSA) applied to second order expansion in 1/ dC (dC is the codimension), extending the seminal work of Le Doussal and Radzihovsky [Phys. Rev. Lett. 69, 1209 (1992)]. In particular, the bending rigidity is found to harden algebraically in the long-wavelength limit with an exponent η=0.789..., which is used to extract the elasticity softening exponent ηu =0.422..., and the roughness exponent ζ=0.605.... The scaling relation ηu =2-2η is proven to hold to all orders in SCSA. Further, applying the SCSA to an expansion in 1/ dC, is found to be essential, as no solution to the self-consistent equations is found in a two-bubble level, which is the naive second-order expansion. Surprisingly, even though the expansion parameter for physical membrane is 1/ dC =1, the SCSA applied to second-order expansion deviates only slightly from the first order, increasing ζ by mere 0.016. This supports the high quality of the SCSA for physical crystalline membranes, as well as improves the comparison to experiments and numerical simulations of these systems. The prediction of SCSA applied to first order expansion for the Poisson ratio is shown to be exact to all orders.

UR - http://www.scopus.com/inward/record.url?scp=70350534420&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.80.041117

DO - 10.1103/PhysRevE.80.041117

M3 - Article

AN - SCOPUS:70350534420

SN - 1539-3755

VL - 80

JO - Physical Review E

JF - Physical Review E

IS - 4

M1 - 041117

ER -