Machine Learning Identification of the Isotropic–Nematic Transition in the Lebwohl–Lasher Model

The Lebwohl-Lasher model [1], consisting of rotor molecules whose axis orientations serve as the degrees of freedom on a simple cubic lattice, provides a powerful framework for studying the isotropic-nematic phase transition in liquid crystals. To identify the first-order transition in this model, we apply machine learning analysis to uncorrelated spatial configurations obtained using standard Metropolis sampling from L × L × L cubic lattices with L = 30 and 60. A convolutional neural network trained on these configurations distinguishes isotropic and nematic phases and reproduces the expected temperature dependence of the scalar order parameter. The network output shows a clear signature of the isotropic-nematic transition, consistent with recent finite-size scaling results [2]. These results highlight the potential of machine learning techniques to complement traditional approaches in studying phase behavior of systems with continuous symmetries.

References

[1] P. A. Lebwohl and G. Lasher. Nematic-liquid-crystal order — a monte carlo calculation. Physical Review A, 6(1):426–429, 1972.

[2] Aojie Xue, Jiahao Xu, D. P. Landau, and K. Binder. Test of universality at first order phase transitions: The lebwohl–lasher model. The Journal of Chemical Physics, 161:134107, 2024.