Eigen Microstate Condensation and Critical Phenomena in the Lennard-Jones Fluid

TL;DR

This paper uses eigen microstate theory to accurately determine the critical point and exponents of the Lennard-Jones fluid, revealing its phase structure and confirming finite-size scaling behavior.

Contribution

It introduces the application of eigen microstate theory to study critical phenomena in Lennard-Jones fluids, providing precise critical parameters and structural insights.

Findings

Critical temperature T_c = 1.188(2)

Critical density ρ_c = 0.320(4)

Critical exponents β = 0.32(2), ν = 0.64(3)

Abstract

Despite extensive study of the liquid-gas 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-gas continuous phase transition in the 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, $T_c = 1.188(2)$, and critical density, $\rho_c = 0.320(4)$. Furturemore, we obtain critical exponents of the LJ fluid, $\beta = 0.32(2)$ and $\nu = 0.64(3)$, 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 system.