Critical crossover functions for simple fluids: towards the crossover modelling uniqueness

International audienceBased on a single non-universal temperature scaling factor present in a simple fluid case, a detailed analysis of non-universal parameters involved in different critical-to-classical crossover models is given. For the infinite limit of the cutoff wave number, a set of three scaling-parameters is defined for each model such that it shows all the shapes of the theoretical crossover functions overlap on the mean crossover function shapes close to the non-trivial fixed point. The analysis of corresponding links between their fluid-dependent parameters opens a route to define a parametric model of crossover equation-of-state, closely satisfying the universal features calculated from the Ising-like limit in the massive renormalization scheme