In 1952, Robin Potts introduced the Potts model in his PhD thesis as a generalisation of the Ising model, which is a simpler model than the Potts model.
The Potts model is a mathematical model that is used to describe a system of interacting particles, which could be things like atoms, molecules, or even pixels in an image. Each particle can take on one of q possible states, where q is some positive integer. For example, in a 2D image, each pixel could be assigned one of q colors.
The energy of the system is determined by the interactions between neighboring particles, which are described by a mathematical function. This function determines how much energy is associated with each possible arrangement of particle states, based on the states of the neighboring particles. In other words, it considers the fact that particles tend to be more likely to have certain states when their neighbors have certain other states.
The Potts model can be used to study a wide range of physical, chemical, and biological systems, as well as to perform image segmentation in computer vision. By analyzing the energy landscape of the system, researchers can gain insights into how the particles interact with each other, and how they behave under different conditions. More precisely, in image segmentation, the Potts model has been used to partition an image into regions that have similar properties (such as color, texture, or intensity). In this case, the particles in the model represent pixels, and the interactions between them are determined by the similarity of their colors. By applying the Potts model to an image, researchers can segment it into distinct regions, which can be useful for tasks like object recognition and tracking. Another example is in protein folding. In this case, the particles in the model represent amino acids, and the interactions between them are determined by the protein’s energy landscape. By simulating the folding process using the Potts model, researchers can gain insights into how proteins fold and how their structures affect their function.
These are just a few examples of the many applications of the Potts model. Its versatility and flexibility make it a useful tool for studying a wide range of systems