In his 1924 PhD thesis, Ising erroneously predicted - based on his investigation into the one-dimensional model - that there were no phase transitions for any lattice dimension d with temperature T>0. However, it has since been shown that abrupt phase transitions occur for lattices with dimensions d>2. In 1944, Lars Onsager published his proof for the two-dimensional Ising model, containing his analytical result for the critical temperature for an infinite lattice.
The investigation involved writing a Python program to implement the Metropolis algorithm for the two-dimensional Ising model. Various properties of the model were obtained using computational methods and compared with the theoretical expectations. In particular; autocorrelation, statistical error, hysteresis, response functions, finite-size scaling, domain size, and finally comparing the Metropolis algorithm to Wolff's cluster-flipping algorithm.