Universality class
Singular behaviors of physical properties around the phase transition point are governed by a few parameters (these parameters are called critical exponents) and the combination of the critical exponents is called universality class. Symmetries and spatial dimensions of the system determine the universality class and details of the system such as strength of interactions and the lattice structures do not change universality class. To determine the universality class of the phase transitions, it is necessary to perform the high-accuracy calculations such as the unbiased Monte Carlo calculations. Unbiased Monte Carlo calculations can be done with ALPS or DSQSS and the estimation of the critical exponents from the numerical data can be done with BSA.