The hobbyhorse of magnetic systems: the Ising model

Abstract

The purpose of this article is to present a detailed numerical study of the\nsecond-order phase transition in the 2D Ising model. The importance of\ncorrectly presenting elementary theory of phase transitions, computational\nalgorithms and finite-size scaling techniques results in a important\nunderstanding of both the Ising model and the second order phase transitions.\nIn doing so, Markov Chain Monte Carlo simulations are performed for different\nlattice sizes with periodic boundary conditions. Energy, magnetization,\nspecific heat, magnetic susceptibility and the correlation function are\ncalculated and the critical exponents determined by finite-size scaling\ntechniques. The importance of the correlation length as the relevant parameter\nin phase transitions is emphasized.\n