One-Dimensional Models

Abstract

The study of one-dimensional (1-D) systems is of interest for two main reasons. First, there are actual systems that are linear, such as linear polymers, proteins, and nucleic acids. Although all of these occupy three-dimensional space, their main properties are determined by the 1-D sequence of units and bonds. Second, these models are usually easily solvable. Therefore some general properties, theorems, conjectures, approximations, and the like may be tested on a 1-D system. The answers we obtain are sometimes also relevant to three-dimensional systems. Finally, the methods used to solve the 1-D partition functions are elegant and in themselves aesthetically satisfying.