The Hobbyhorse of Magnetic Systems: The Ising Model

Abstract

The purpose of this article is to present a detailed numerical study of the second-order phase transition in the 2D Ising model. The importance of correctly presenting elementary theory of phase transitions, computational algorithms and finite-size scaling techniques results in a important understanding of both the Ising model and the second order phase transitions. In doing so, Markov Chain Monte Carlo simulations are performed for different lattice sizes with periodic boundary conditions. Energy, magnetization, specific heat, magnetic susceptibility and the correlation function are calculated and the critical exponents determined by finite-size scaling techniques. The importance of the correlation length as the relevant parameter in phase transitions is emphasized.

arXiv comment15 pages, 15 figures

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• Rejection-free Glauber Monte Carlo for the 2D Random Field Ising Model via Hierarchical Probabilistic Counters