First order transition in the Lebwohl-Lasher model: a testing ground for a newly discovered universality.

The Lebwohl-Lasher model [1] on simple cubic lattices provides a good testing ground for a first order universality which was newly discovered for the spin-flop transition in a 3D anisotropic Heisenberg antiferromagnet in a field [2]. In the finite size scaling at the first order transition in both models, a degeneracy factor, 𝑞, was introduced phenomenologically and predicts the universal intersection of the 4th order cumulants of the order parameter. The factor 𝑞 does not depend on the specifics of the models, implying an unknown first order universality. For the Lebwohl-Lasher model, the theory predicts 𝑞 = 4𝜋. Careful Monte Carlo simulations were performed on lattices with various sizes, and good agreement between theory and simulations on the value of the intersection has been obtained, which further supports the concept of first order universality.

[1] P. A. Lebwohl and G. Lasher, Phys. Rev. A 6, 426 (1972).

[2] J. Xu, S.-H. Tsai, D. P. Landau, and K. Binder, Phys. Rev. E 99, 023309 (2019).

*Kurt Binder, our friend and long time collaborator, passed away in late 2022 after this research had begun.