Linear aggregation beyond isodesmic symmetry

TL;DR

This paper demonstrates that certain real-world linear aggregation systems, often thought to break isodesmic symmetry, can be modeled and exactly solved using a class of one-dimensional models similar to the Ising model.

Contribution

It introduces a class of exactly solvable one-dimensional models that extend beyond traditional isodesmic symmetry, providing new insights into linear aggregation.

Findings

Examples of real systems mapped to these models

Exact solutions for the extended models

Insights into symmetry breaking in aggregation

Abstract

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.