ISO-g((2)) processes in equilibrium statistical mechanics

The pair correlation function g((2))(r) in a classical many-body system dep ends in a nontrivial way both on the number density rho and on the pair int eractions v(r), and a long-standing goal of statistical mechanics has been to predict these effects quantitatively. The present investigation focuses on a restricted circumstance whereby simultaneous isothermal changes in rho and v(r) have exactly canceling effects on g(2). By appealing to the isoth ermal compressibility relation, we establish that an upper limit for densit y increase exists for this "iso-g((2))" process, and at this limit in three dimensions the correspondingly modified pair interaction develops a long-r anged Coulombic character. Using both the standard hypernetted chain and Pe rcus-Yevick approximations, we have examined the iso-g((2)) process for rig id rods in one dimension that starts at zero density, and maintains the sim ple step-function pair correlation during density increase, a process that necessarily terminates at a covering fraction of one-half. These results ha ve been checked with detailed Monte Carlo simulations. We have also estimat ed the effective pair potentials that are required for the corresponding ri gid-sphere model in three dimensions, for which the simple step-function pa ir correlation can be maintained up to a covering fraction of one-eighth.