  Exactly solvable models of linear aggregation have been known since Ising's
seminal one-dimensional model. This model is defined by a unique
nearest-neighbour bond strength that is independent of the length of the
cluster; known as isodesmic symmetry. Linear aggregation in real systems has
often been associated with broken isodesmic symmetry. Here we show that
important examples can be mapped to a class of one-dimensional models that are
also exactly solvable.
