Project Selection

Supervisor meeting 19/10/17

After a meeting with my supervisor over a cup of coffee, the following outcomes were reached:

• The project will be on the Ising model.
• The models will be run using python.
• If feasible, a Beowulf cluster will be put together using old PCs from DIT to run later simulations (will deal with later on in the project).

The Ising Model 

The Ising model is a branch of statistical mechanics. The model describes a magnetic phase transition that separates an order phase from a disorder phase. The main ingredient of the Ising model is the energy of a pair of spins. The spins could be that of an electron, atom, molecule or anything that makes up the material. The spin can only contain 2 possible values, up or down. The Ising model tells us on each bond between spins the energy of the bonds are minimized when the 2 spins are aligned.  It is the simplest model of the interactions between the spins in a material. It gives ability to display the phase transition of the material from ferromagnetic to paramagnetic.  

For example if we take Iron, at low temperatures (low depending on the characteristics of the material) the spins will be pointing in the same direction and the sample is said to be ferromagnetic. As the temperature is increased some spins begin to flip until the critical temperature is reached which is known as the curie temperature. At this point the spin orientation is random and the sample is now paramagnetic.

This model was suggested to Ising by his thesis adviser, the famous German physicist Wilhelm Lenz. Ising solved the one dimensional model and on the basis that the 1D model had no phase transition, he asserted that there was no phase transition in any dimension. This unfortunately is false. However what could be considered worse for Ising is that the model that takes his name is almost universally mispronounced as "I-Zing". Ising’s name is correctly pronounced as "E-zing"!

Programming language 

The language that is to be used to simulate the model will be python which is a popular high level language, for general purpose programming. I personally have never used python having only dealt with C, C++, Mathlab, and Java. This new challenge is exciting to me as I always love expanding my software portfolio. I have set up Python 3.6.3 on my PC and I have even written my first piece of Python code:

Which garnered some interesting results