Revisiting universality of the liquid-gas critical point in 2D

Abstract

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. This stimulated the ongoing debate about the nature of the universality class of the transition -- lasting since the creation of the theory of scaling. We revisit the conjecture that the LG criticality is that of the Ising model. Large scale Monte Carlo simulations of the LG criticality in 2D free space in combination with the numerical flowgram method give the critical indices agreeing with the Onsager values within the error of 1\%. The related problem about the role of higher order odd terms in the (real) $\varphi^4$ field model is addressed too. The scaling dimension of the $\varphi^5$ term at criticality is shown to be the same as of the linear one $\varphi$. We suggest that the role of all higher order odd terms is simply in generating the linear field operator at the criticality.