The mechanism of the online user preference evolution is of great significance for understanding the online user behaviors and improving the quality of online services. Since users are allowed to rate on objects in many online systems, ratings can well reflect the users preference. With two benchmark datasets from online systems, we uncover the memory effect in users selecting behavior which is the sequence of qualities of selected objects and the rating behavior which is the sequence of ratings delivered by each user. Furthermore, the memory duration is presented to describe the length of a memory, which exhibits the power-law distribution, i.e., the probability of the occurring of long-duration memory is much higher than that of the random case which follows the exponential distribution. We present a preference model in which a Markovian process is utilized to describe the users selecting behavior, and the rating behavior depends on the selecting behavior. With only one parameter for each of the users selecting and rating behavior, the preference model could regenerate any duration distribution ranging from the power-law form (strong memory) to the exponential form (weak memory).
Considering different universality classes of the QCD phase transitions, we perform the Monte Carlo simulations of the 3-dimensional $O(1, 2, 4)$ models at vanishing and non-vanishing external field, respectively. Interesting high cumulants of the order parameter and energy from O(1) (Ising) spin model, and the cumulants of the energy from O(2) and O(4) spin models are presented. The critical features of the cumulants are discussed. They are instructive to the high cumulants of the net baryon number in the QCD phase transitions.
