A team of researchers of HSE University’s Tikhonov Moscow Institute of Electronics and Mathematics (Professor Lev Shchur, Assistant Professor Evgeny Burovsky, and doctoral student Maria Guskova), in collaboration with Prof. Wolfhard Janke (Leipzig University, Germany), has made a new discovery about the properties of classical Monte Carlo (MC) algorithms. The team identified an interesting connection between the properties of the algorithm used and the properties of statistical systems that are modeled using the algorithm. As it turns out, the acceptance rate in local Metropolis and heat-bath algorithms appear to be a linear function of internal energy of the used model. Moreover, the researchers were able to prove analytically that, for a one-dimensional (1D) Ising model, the acceptance rate of the Metropolis algorithm is a linear function of internal energy. This proved true not only for the thermodynamic limit, but for an arbitrary size of the system under study as well. A computational experiment demonstrated that, for all analyzed spin models with different types of interaction in any space dimensions, the linearity is performed around the phase transition point.