In this paper we use non-Gaussian hydrodynamics to study the magnetic respo
nse of a flux-line liquid in the mixed state of a type-II superconductor. B
oth the derivation of our model, which goes beyond conventional Gaussian fl
ux liquid hydrodynamics, and its relationship to other approaches used in t
he literature are discussed. We focus on the response to a transverse tilti
ng field which is controlled by the tilt modulus c(44) of the Aux array. We
show that interaction effects can enhance c(44) even in infinitely thick c
lean materials. This enhancement can be interpreted as the appearance of a
disentangled flux-liquid fraction. In contrast to earlier work, our theory
incorporates the nonlocality of the intervortex interaction in the field di
rection. This nonlocality is crucial for obtaining a nonvanishing renormali
zation of the tilt modulus in the thermodynamic limit of thick samples. [S0
163-1829(99)00909-1].