Thermodynamic metric geometry and the Fisher-Widom line of simple fluids

Two boundary lines are frequently discussed in the literature, separating state regions dominated by repulsion or attraction. The Fisher-Widom line indicates where the longest-range decay of the total pair correlation function crosses from monotonic to exponentially damped oscillatory. In the context of thermodynamic metric geometry, such a transition exists where the Ricci curvature scalar vanishes, R = 0. To establish a possible relation between these two lines, R is worked out for four simple fluids. The truncated and shifted Lennard-Jones, a colloid-like and the square-well potential are analyzed to investigate the influence of the repulsive nature on the location of the R = 0 line. For the longer-ranged Lennard-Jones potential, the influence of the cutoff radius on the R = 0 line is studied. The results are compared with literature data on the Fisher-Widom line. Since such data are rare for the longer-ranged Lennard-Jones potential, dedicated simulations are carried out to determine the number of zeros of the total correlation function, which may provide approximate information about the position of the FisherWidom line. An increase of the repulsive strength toward hard sphere interaction leads to the disappearance of the R = 0 line in the fluid phase. A rising attraction range results in the nonexistence of the Fisher-Widom line, while it has little effect on the R = 0 line as long as it is present in the fluid state.