Strong and Weak Field Criticality of Liquid Gas Transition in 2D

Finite size scaling (FSS) analysis of the liquid gas criticality is complicated by the absence of any broken symmetry. This, does not allow a straightforward finding of the coexistence line and the critical point -- especially in 2D. The numerical flowgram (NF) method[1] is adapted for a controlled determination of the boundary between weak and strong field critical regions by applying classical Monte Carlo to the square well model. This boundary coincides with the coexistence line of the liquid-gas transition with respect to the leading scaling behavior. The NF method allows measuring the critical indices μ, ν within 1-2% of the total error. Furthermore, the NF allows testing the so called complete scaling theory of the critical point[2] without tuning the system into the coexistence line. This theory predicts linear mixing between the primary scaling operators and pressure. We show that the NF analysis should see corrections to scaling which are stronger than the standard ones of the 2D Ising model. It can also resolve the non analytical correction to the diameter.

[1] A.B. Kuklov, N.V. Prokof’ev, B.V. Svistunov, M. Troyer, Ann. Phys., 321, 1602 (2006)
[2] M. E. Fisher and G. Orkoulas, Phys. Rev. Lett., 85, 696 (2000)