Eigen-microstate condensation and critical phenomena in the Lennard-Jones fluid

Despite extensive study of the liquid-vapor phase transition, accurately determining the critical point and the critical exponents in fluid systems through direct simulation remains a challenge. We employ the eigen-microstate theory (EMT) to investigate the liquid-vapor continuous phase transition in Lennard-Jones (LJ) fluid within the canonical ensemble. In EMT, the probability amplitudes of eigen-microstates serve as the order parameter. Using finite-size scaling of probability amplitudes, we simultaneously determine the critical temperature, Tc = 1.188(2), and critical density, ρc = 0.320(4), for an LJ potential truncated at Rc = 2.5σ. Furthermore, we obtain critical exponents of the LJ fluid, β = 0.32(2) and ν = 0.64(3), which demonstrate a great agreement with the Ising universality class. This method also reveals the mesoscopic structure of the emergent phase, characterizing the three-dimensional (3D) spatial configuration of the fluid in the critical region. This work also confirms the finite-size scaling behavior of the probability amplitudes of the eigen-microstates in the critical region. The EMT provides a powerful tool for studying the critical phenomena of complex fluid systems.