A SYSTEM OF N-INTERACTING FERMIONS AND ITS UNUSUAL N-]0 LIMIT

We consider a U(n) model of fermions in 1 + 1 dimensions at finite density, with an attractive delta function interaction. This model appears in the replica analysis of a system of fermions in a random time-dependent potential. It can also be mapped to the problems of steps on vicinal crystal surfaces, commensurate to incommensurate transitions, and superconducting flux lines, all in two dimensions with quenched disorder. To understand the nature of these phases, we compute the U(n) symmetric analogues of particle-hole excitations using Bethe ansatz techniques. We find that, in the n --> 0 limit, the particle density of states vanishes while the holes behave just as in the pure problem. A naive argument then suggests that the fermion density-density correlations scale as 1/r. This in turn implies that if the fermion lines are regarded as domain walls advancing an order parameter, the resulting order is destroyed (i.e. has exponentially decaying correlations).