ABSTRACT
In addition, real systems have many parameters but often only a few of them govern their main properties. Simulations can help identify relevant mechanisms before realizing experimental setups or constructing theoretical models. In many cases, numerical simulations are the only way to study very complex systems that theory and experiment cannot investigate properly. In a first-order transition, for a sufficiently large, the energy and the magnetization are discontinued at the transition; the heat capacity and the susceptibility therefore cannot be defined at the transition. Finite-size effects on thermodynamic quantities and on spin–spin correlation have been shown by a renormalization group analysis. The Metropolis algorithm which updates spin after spin will take a long time to consider unnecessarily all spins in a cluster because, except for a small fraction at spins at the boundary, the spins in a cluster do not need to change orientation.
