Abstract
The aim of this short review is to present an overview of problems involving random surfaces on a cubic lattice: why one studies them, what questions one tries to answer, what assumptions are made in the models, what one computes to understand these models, and some things that have been learned. The emphasis will be on what one can calculate and why the problem is computationally intensive but tractable. There has also been considerable progress in rigorous treatments of this subject; this train of work will be discussed in the following paper. Since there have been some rather extensive reviews [1][2][3][4] on the subject, there is no need to be encyclopedic. Liberal use is made of these sources as well as unpublished lecture notes by A. Maritan [5] and E. Orlandini [6].
Based on work in collaboration with E. Orlandini, I. Beichl, F. Sullivan, M.C. Tesi, J. O’Connell, D. Libes, U. Glaus, A. Maritan, and J.R. Banavar.
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Einsteint, T.L., Stella, A.L. (1998). Survey of Self-Avoiding Random Surfaces on Cubic Lattices: Issues, Controversies, and Results* . In: Whittington, S.G., De Sumners, W., Lodge, T. (eds) Topology and Geometry in Polymer Science. The IMA Volumes in Mathematics and its Applications, vol 103. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1712-1_12
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