1998/08/19 by Mark J. Bowick, Mark Bowick, Alex Travesset · 1 citation
Mathematics · Physics and Astronomy · #Anisotropy #Combinatorics #Computer science #Condensed matter physics #Critical dimension #Critical exponent #Critical point (mathematics) #Dimension (graph theory) #Embedding #Exponent #Geometry #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Phase (matter) #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum mechanics #Renormalization group #Statistical physics #Symmetry (geometry) #Theoretical and Computational Physics #cond-mat.soft
paper · pdf · doi:10.1103/physreve.59.5659
published as Phys. Rev. E59 (1999) 5659 · 38 pages, 31 Postscript figures, uses epsf
arxiv created 1998/08/19 · openalex publication_date 1999/05/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We analyze the tubular phase of self-avoiding anisotropic crystalline membranes. A careful analysis using renormalization group arguments together with symmetry requirements motivates the simplest form of the large-distance free energy describing fluctuations of tubular configurations. The non-self-avoiding limit of the model is shown to be exactly solvable. For the full self-avoiding model we compute the critical exponents using an epsilon expansion about the upper critical embedding dimension for general internal dimension D and embedding dimension d. We then exhibit various methods for reliably extrapolating to the physical point (D=2,d=3). Our most accurate estimates are nu=0.62 for the Flory exponent and zeta=0.80 for the roughness exponent.