Ising model with super long-range interactions ⚡️

This repository includes:

• pdf with an analytic analysis of the model and an exploration of the Monte Carlo simulation results.
• Python code to run MC simulations of the model (for the case of zero field).

This was initally developed as a project for my Statistical Physics course, with a later revision to improve it.

Running the code

1. Simply run main.py. Input the number of spins and the number of Monte Carlo steps to perform. I recommend starting with 50 spins and 10000 steps.
2. Once finished, a folder is created with the results of the run: A file with the mean magnetization per spin and total energy of each of the MC samples, for each of the temperatures. Be careful with over-writing previous results.

An example of the output is found in the folder N50.

Processed results from MC simulations

Analytical results (see pdf)

Some of the relevant equations found in the project:

$$\begin{matrix} E = \frac{J}{2} - HM - \frac{J}{2N} M^2 & m = \tanh{ \left( \frac{J}{k_BT} (m + \frac{H}{J}) \right)} \\ c_V(T,H) = \frac{J}{T} \frac{1-m^2}{m^2 - \left( 1-\frac{k_B T}{J} \right)} \left( m^2 + \frac{H}{J}m\right) & \chi _M(T, H) = \frac{1}{J} \frac{1-m^2}{m^2-\left( 1- \frac{k_B T}{J}\right)} \end{matrix}$$