Finite-size scaling of interface free energies in the 3d Ising model

Finite Size Scaling (FSS) is a very powerful tool, particularly useful in extracting numerical estimates from Monte Carlo simulations. Numerical simulations give results on systems of finite size, where phase transitions cannot occur. Thus, a fundamental task in Monte Carlo studies of phase transitions is the extraction of results holding in the thermodynamic limit from data obtained in systems of finite size. FSS describes how a system of finite size approaches criticality in the thermodynamic limit. One of its most far– reaching aspects concerns the universality of the FSS functions. If universality holds, complex systems share the same critical behaviour as simpler systems. This opens the possibility to use simple models to obtain accurate information on much more complicated theories. In a recent paper[1], a study of the FSS of spatial ’t Hooft loops of maximal size across the deconfinement phase transition has been performed in the SU(2) Yang–Mills theory. By this analysis, a numerical estimate of the dual string tension for the first time observed in [2] has been obtained. Moreover, also the FSS of the electric free energies of the theory has been investigated. According to the Svetitsky–Yaffe conjecture[3], the 4d SU(2) Yang–Mills theory at the deconfinement transition is believed to be in the same universality class as the 3d Ising model at the