Book Chapter

Effect of Confinement: Polygons in Strips, Slabs and Rectangles

Anthony J Guttmann, Iwan Jensen

POLYGONS, POLYOMINOES AND POLYCUBES | Lecture Notes in Physics | SPRINGER-VERLAG BERLIN | Published : 2009

Abstract

In this chapter we will be considering the effect of confining polygons to lie in a bounded geometry. This has already been briefly discussed in Chapters 2 and 3, but here we give many more results. The simplest, non-trivial case is that of SAP on the two-dimensional square lattice ℤ2, confined between two parallel lines, say x = 0 and x = w. This problem is essentially 1-dimensional, and as such is in principle solvable. As we shall show, the solution becomes increasingly unwieldy as the distance w between the parallel lines increases. Stepping up a dimension to the situation in which polygons in the simple-cubic lattice ℤ3 are confined between two parallel planes, that is essentially a two..

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