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This monograph gives a detailed introductory exposition of research
results for various models, mostly two-dimensional, of directed
walks, interfaces, wetting, surface adsorption (of polymers),
stacks, compact clusters (lattice animals), etc. The unifying
feature of these models is that in most cases they can be solved
analytically. The methods used include transfer matrices,
generating functions, recurrence relations, and difference
equations, and in some cases involve utilization of less familiar
mathematical techniques such as continued fractions and q-series.
The authors emphasize an overall view of what can be learned
generally of the statistical mechanics of anisotropic systems,
including phenomena near surfaces, by studying the solvable models.
Thus, the concept of scaling and, where known, finite-size scaling
properties are elucidated. Scaling and statistical mechanics of
anisoptropic systems in general are active research topics. The
volume provides a comprehensive survey of exact model results in
this field.
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