Revisiting universality of the liquid-gas critical point in two dimensions

Critical point of liquid-gas (LG) transition does not conform with the paradigm of spontaneous symmetry breaking because there is no broken symmetry in both phases. We revisit the conjecture that this critical point belongs to the Ising class by performing large scale Monte Carlo simulations in two-dimensional free space in combination with the numerical flowgram method. Our main result is that the critical indices do agree with the Onsager values within the error of 1%-2%. This significantly improves the accuracy reported in the literature. The related problem about the role of higher order odd terms in the (real) φ^{4} field model as a mapping of the LG transition is addressed too. The scaling dimension of the φ^{5} term at criticality is shown to be the same as that of the linear one φ. We suggest that the role of all higher order odd terms at criticality is simply in generating the linear field operator with the critical dimension consistent with the Ising universality class.