11Ising Model
The systems we have considered so far are either ideal or close to ideal. The interaction between particles is either absent or sufficiently weak to change the thermodynamic properties only slightly. In the several chapters that follow, we extend our statistical methods to systems consisting of strongly interacting particles. Usually, the strong interaction is between a pair of nearest neighbors or between a pair in close proximity.
In this chapter, we learn an Ising model as the simplest model for strongly interacting particles. The Ising model and its variations are usually for magnets. Spontaneous magnetization in a ferromagnet is due to strong interactions between nearby electron spins that favor aligned spin orientations. The Ising model originates in a magnetic system, and the relevance of the model to the magnetic systems still remains. Here we learn the Ising model, because there are many systems in chemistry and biochemistry that can be recast into the Ising model.
In Section 11.1, we introduce the model, and look at how some systems in chemistry and biochemistry are recast into the model. In Section 11.2, we calculate the partition function for small systems in one dimension. Approximation methods we learn in Section 11.3 allow us to obtain the partition function of the system with many particles and calculate some average quantities. Section 11.4 covers a method of a transfer matrix for the exact calculation of the partition function. In Section 11.5 ...