Fluids of core-softened particles in dimension 2: an integral equation study

An interaction model with core-softening that produces clustered phases in dimension 2 is studied by integral equation theories, and compared with corresponding simulation results. It is shown that the Hypernetted-chain (HNC) equation is surprisingly accurate and easier to solve numerically than the Percus-Yevick (PY) equation, which appears unable to operate in the cluster phase region. A comparison is made of the behaviour of the two theories in the absence of core-softening: in the high-temperature regime the Percus-Yevick theory is more accurate, whereas in the low-temperature regime it is HNC theory that becomes more accurate. It is the inclusion of an infinite class of cluster diagrams that allows the latter theory to better describe phases where local structures and small clusters play a predominant role in characterizing their macroscopic properties. The contrasting behaviour observed for continuous phases of hard and soft interactions must be due to fortuitous diagram compensations in the real system. HNC theory gives a very accurate structural description of the various cluster phases, as shown by comparing the radial distribution functions and structure factors with those from simulation.