Nonlocal effective-average-action approach to crystalline phantom membranes

Journal Article · Tue Mar 15 00:00:00 EDT 2011 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PHYSREVE.83.031137· OSTI ID:21560068

Hasselmann, N ^[1]; Braghin, F L ^[2]

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1. Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart (Germany)
2. International Institute of Physics, Universidade Federal do Rio Grande do Norte, 59072-970, Natal, RN (Brazil)

We investigate the properties of crystalline phantom membranes, at the crumpling transition and in the flat phase, using a nonperturbative renormalization group approach. We avoid a derivative expansion of the effective average action and instead analyze the full momentum dependence of the elastic coupling functions. This leads to a more accurate determination of the critical exponents and further yields the full momentum dependence of the correlation functions of the in-plane and out-of-plane fluctuation. The flow equations are solved numerically for D=2 dimensional membranes embedded in a d=3 dimensional space. Within our approach we find a crumpling transition of second order which is characterized by an anomalous exponent {eta}{sub c}{approx_equal}0.63(8) and the thermal exponent {nu}{approx_equal}0.69. Near the crumpling transition the order parameter of the flat phase vanishes with a critical exponent {beta}{approx_equal}0.22. The flat phase anomalous dimension is {eta}{sub f}{approx_equal}0.85 and the Poisson's ratio inside the flat phase is found to be {sigma}{sub f}{approx_equal}-1/3. At the crumpling transition we find a much larger negative value of the Poisson's ratio {sigma}{sub c}{approx_equal}-0.71(5). We discuss further in detail the different regimes of the momentum dependent fluctuations, both in the flat phase and in the vicinity of the crumpling transition, and extract the crossover momentum scales which separate them.

• OSTI ID: 21560068
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Vol. 83, Issue 3; Other Information: DOI: 10.1103/PhysRevE.83.031137; (c) 2011 American Institute of Physics; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANOMALOUS DIMENSION
CORRELATION FUNCTIONS
CRYSTALS
FLOW MODELS
FLUCTUATIONS
MEMBRANES
NONLOCAL POTENTIAL
ORDER PARAMETERS
RENORMALIZATION
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS
DIMENSIONLESS NUMBERS
FUNCTIONS
MATHEMATICAL MODELS
POTENTIALS
SCALE DIMENSION
VARIATIONS