Freezing of the classical two-dimensional, one-component plasma

Abstract

The results of a study of freezing in the two-dimensional, one-component plasma are reported. The analysis is based on a nonlinear integral equation for the singlet density in an inhomogeneous system. The existence and location of the freezing transition are obtained both from a bifurcation theory approach and by imposing equality of grand thermodynamic potentials of the liquid and crystalline phases. The value of the plasma parameter Γ≡[e2(πρ) 1/2 /kBT] corresponding to the first appearance of long-range crystalline order in the system, found by locating the bifurcation point of the nonlinear equation, is 124. The freezing transition defined by equating the grand potentials of the fluid and crystalline phases is at Γ=133. These values compare well with those found in recent experiments and computer simulations. The bifurcation approach also predicts, correctly, that the first order freezing transition occurs with zero change in volume. The entropy change on freezing predicted by the imposition of the equality of grand potentials is −0.97 kB per particle, about threefold larger than the value obtained from computer simulations. Possible sources of this discrepancy and the relationship between the bifurcation theory and thermodynamic constraint approaches are discussed.