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Statistical Mechanics of Tethered Surfaces
Abstract
We study the statistical mechanics of two-dimensional surfaces of fixed connectivity embedded in $d$ dimensions, as exemplified by hard spheres tethered together by strings into a triangular net. Without self-avoidance, entropy generates elastic interactions at large distances, and the radius of gyration ${R}_{G}$ increases as ${(\mathrm{ln}L)}^{\frac{1}{2}}$, where $L$ is the linear size of the uncrumpled surface. With self-avoidance ${R}_{G}$ grows as ${L}^{\ensuremath{\nu}}$, with $\ensuremath{\nu}=\frac{4}{(d+2)}$ as obtained from a Flory theory and in good agreement with our Monte Carlo results for $d=3$.
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Cited by
Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
Bouchaud, J.-P., & Georges, A. (1990) · Physics Reports · doi:10.1016/0370-1573(90)90099-n · Cited by 4,162
Two‐Dimensional Polymers: Just a Dream of Synthetic Chemists?
Sakamoto, J., van Heijst, J., Lukin, O., & Schlüter, A. D. (2009) · Angewandte Chemie International Edition · doi:10.1002/anie.200801863 · Cited by 734
Fluctuations in membranes with crystalline and hexatic order
Nelson, D. R., & Peliti, L. (1987) · Journal de Physique · doi:10.1051/jphys:019870048070108500 · Cited by 676
Self-citationScaling Properties of Stretching Ridges in a Crumpled Elastic Sheet
Lobkovsky, A., Gentges, S., Li, H., Morse, D., & Witten, T. A. (1995) · Science · doi:10.1126/science.270.5241.1482 · Cited by 392
Shapeable sheet without plastic deformation
Oppenheimer, N., & Witten, T. A. (2015) · Physical Review E · doi:10.1103/physreve.92.052401 · Cited by 18
Metadata
- Authors
- Kantor, Y., Kardar, M., & Nelson, D. R.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1986-08-18
- Volume
- 57
- Issue
- 7
- Pages
- 791-794
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2066443345
- Cited by
- 314
- References
- 0
- FWCI
- 11.08
- Type
- journal article
- Language
- en
- Open access
- closed
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