English

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

Statistical Mechanics 2026-01-19 v1 Data Analysis, Statistics and Probability

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, Tc=1.188(2)T_c = 1.188(2), and critical density, ρc=0.320(4)\rho_c = 0.320(4). Furturemore, we obtain critical exponents of the LJ fluid, β=0.32(2)\beta = 0.32(2) and ν=0.64(3)\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.

Keywords

Cite

@article{arxiv.2601.10741,
  title  = {Eigen Microstate Condensation and Critical Phenomena in the Lennard-Jones Fluid},
  author = {Lan Yang and Zhaorong Pang and Chongzhi Qiao and Gaoke Hu and Jiaqi Dong and Rui Shi and Xiaosong Chen},
  journal= {arXiv preprint arXiv:2601.10741},
  year   = {2026}
}