Phase diagram of a classical fluid in a quenched random potential

– We consider the phase diagram of a classical fluid in the presence of a random pinning potential of arbitrary strength. Introducing replicas for averaging over the quenched disorder, we use the hypernetted chain approximation to calculate the correlations in the replicated liquid. The freezing transition of the liquid into a nearly crystalline state is studied using a density functional approach, and the liquid-to-glass transition is studied using a phenomenological replica symmetry breaking approach introduced by Mézard and Parisi. The first-order liquid-to-crystal transition is found to change to a continuous liquid-to-glass transition as the strength of the disorder is increased above a threshold value. The equilibrium phase diagram of a classical system of interacting particles in the presence of quenched pinning potential is a subject of much current interest, in view of understanding the behavior of various systems such as magnetic bubble arrays [1], Wigner crystals of electrons [2], and flux lines in the mixed phase of high-Tc superconductors [3]. In particular, for layered type-II superconductors such as Bi2Sr2CaCu2O8 in a magnetic field H perpendicular to the layers, the (T,H) phase diagram is especially interesting. The flux lines in these materials may be viewed as columns of interacting “pancake” vortices residing on the layers, and the properties of the mixed phase may be described in terms of the classical statistical mechanics of these point-like objects. At low enough fields, a first-order melting transition separates an ordered vortex lattice from a disordered “vortex liquid” state [4]. Existing theoretical studies [5,6] suggest that weak point disorder only slightly distorts the crystalline state, leading to the observed “Bragg glass” phase with quasi–long-range translational order [7]. The freezing line of a layered system of pancake vortices in the presence of weak point pinning has been (∗) Laboratoire associé à l’Université Joseph Fourier.