Monte Carlo simulations of fluids whose particles interact with a logarithmic potential.

Monte Carlo simulations of a model fluid in which the particles interact via a continuous potential that has a logarithmic divergence at a pair separation of σ, which we introduced in J. G. Powles et al., Proc. R. Soc. London, Ser. A 455, 3725 (1999), have been carried out. The potential has the form, [lowercase_phi_synonym](r)=-ε ln(f(r)), where ε sets the energy scale and f(r)=1-(σ/r)^m. The value of m chosen was 12 but the qualitative trends depend only weakly on the value of m, providing it is greater than 3. The potential is entirely repulsive and has a logarithmic divergence as ∼-ln(r/σ-1) in the r→σ limit. Predictions of the previous paper that the internal energy can be computed at all temperatures using the standard statistical mechanics formula for continuous potentials are verified here. The pressure can be calculated using the usual virial expression for continuous potentials, although there are practical limitations in resolving the increasingly important contribution from the r→σ limit at reduced temperatures greater than ∼5. The mean square force ≤F²≥ and infinite frequency shear G_∞ and bulk K_∞ moduli are only finite for T^*=k_BT/ε<1. The logarithmic fluid’s physical properties become increasingly more like that of the hard sphere fluid with increasing temperature, showing a sharp transition in the behavior of the mean square force and infinite frequency elastic constants at T^*=1. The logarithmic fluid is shown to exhibit a solid-fluid phase transition. [ABSTRACT FROM AUTHOR]