Physica A 175 (1991) 222-228 North-Holland SEARCH FOR LIQUID-GAS TRANSITION ABOVE THE CRITICAL TEMPERATURE Joan ADLER and D. STAUFFER Physics Department, Teclmion, Haifa 32000, Israel and School of Physics and Astronomy. Raymond Beverly Sackler Faculty of Exact Sciences, Tel Aviv b'niversity, Ramat Aviv 69978, Israel Received 5 February 1991 Existing series expansions for the two-dimensional lattice gas (lsing magnet) are analyzed above the critical temperature in search for a sharp transition line, where the convergence behavior of a Taylor expansion changes. This transition is expected to appear at the "Kertdsz line" where the droplet surface tension vanishes. In this paper we present claims that we have found numerical indications of sharp transition lines between liquid and gaseous states, even above the critical temperature. Since the 1873 thesis of van der Waals, a crucial aspect of critical phenomena is the continuity of liquid and gaseous states of matter: We can move in the pressure-temperature diagram continuously from the vapor phasc of a fluid at T < T c (where T~ is the critical point of the transition) along a path encircling the critical point towards the liquid side of the coexistence curve at T < T c again, without crossing any jump in the density or singularity in the specific heat. For the lattice gas (spin-½ Ising model) approximation of a fluid, Lee and Yang [1] proved that non-analyticities can happen only for zero field H, i.e. for the chemical potential corresponding to the coexistence curve. Indeed, the droplet model [2a, 3] (for a recent review, see ref. [26]) predicts at zero field and T< Tca very weak "essential" singularity where the Taylor expansion of the density (magnetization) in powers of the field H exists but has zero radius of convergence. T7 ~-6~_ [41 ~.=,t=~z 1'~1, on the basis of improved droplet definitions and simulations for the Ising model [5], pointed out the existence of a sharp transition line above T,, different from the coexistence curve (zero field line) below Tc. For temperatures below this "Kertdsz line", the droplets have a finite surface tension, whereas for higher temperatures, the surface free energy of these droplets is proportional to the bulk energy, similar to lattice animals ]n percolation theory 161. We give a schematic illustration of the topology for 0378-4371/91/$03.5~1 ~ 1991 - El~vier ~'ience Publishers B.V. (North-Holland)