Why the Ising and continuous-space models of ionic systems exhibit essentially different critical behavior

A Landau-Ginzburg-Wilson functional of two order-parameters-the density of charge phi and the density of mass rho -is constructed for ionic systems in which the positions of ions are either in the Euclidean space or are restricted to the lattice sites. We find two phase-transitions: (i) a line of continuous transitions to the charge-ordered phase, induced by the fluctuations phi (r)(proportional to)cos(r .k) with 2 pi /k of molecular size, which terminates at a tricritical point and (ii) a transition between two uniform, ion-poor and ion-rich phases, induced by the whole spectrum of the charge fluctuations. Due to the dominant role of the short-wavelength charge fluctuations, the positions of the transitions depend significantly on the short-distance properties of the system. In different systems (continuous or on different lattices) one or the other transition may be preempted by the occurrence of the other, by which qualitatively different phase diagrams are obtained. (C) 2000 American Institute of Physics.