Ferromagnetic substances are those substances in which the electrons have the tendency to align their spins in a common direction. The Ising model is a mathematical model used for the modelling of ferromagnetic substances. This can be done both analytically and computationally.
In this project we solve this model computationally using the Metropolis algorithm which is a type of Monte Carlo algorithm. Furthermore, we have studied the various thermodynamic properties of the system such as energy, entropy, specific heat and magnetization as a function of temperature in case of both absence and presence of an external magnetic field. Analytical solution has also been discussed in case of no external magnetic field by defining the partition function which further helps us to find the probability for all states to be UP over temperature which in turn gives us an idea of why no phase transition is observed in case of 1-D Ising model in absence of external magnetic field.
Project completed as part of the 'Statistical Mechanics' course in my bachelor's.