Phase transition in 2D and 3D Ising model by time-series analysis

The critical temperatures for 2D and 3D ferromagnetic Ising model are well-known using several methods. In the present paper we introduce a new technique: to study the time-series of different order parameters established by means of a single-spin Monte Carlo evolution of the system in a prefixed thermal bath. Temperature of the simulations is changed as to include a broad range around the critical temperature. We will show that the autocorrelation functions for different sizes of square and cubic lattices intersect in a way similar to the Binder cumulant of the same parameter. This opens new possibilities to study phase transitions by locating the order parameter and the time window leading to the best resolution. Moreover, we will also discuss initial applications of this technique to the Edwards-Anderson model in 2D.