ABSTRACT
In the last two chapters we discussed ideal gas systems where atoms and molecules do not interact with each other—they behave like phantom particles that can pass through one another. This assumption is clearly unrealistic. Real atoms and molecules interact with each other and interact strongly, both through short range and long range potentials. However, when interaction is turned on, it becomes hard to evaluate partition function and the thermodynamic functions from first principles, even within any reasonable approximations. Fortunately, there is a class of restrictive models for which partition function and the thermodynamic functions can be obtained fairly accurately. This happens if the spatial positions of the atoms and/or molecules are restricted to a lattice. These classes of models are called lattice models. These models are of great value in understanding many properties of solids. Here we are particularly interested in them due to their accessibility to analytical solution that in turn allows in depth understanding of the role of interactions in giving rise to such phenomena as phase transitions and critical phenomena. Study of lattice models has many other benefits in terms of learning techniques of Statistical Mechanics. Historically the first such model was proposed by Ising in 1925 [1] to explain the magnetic properties of solids. Since then the Ising model has become one of the main tools to understand various properties of many body interacting systems.
