We compute the ground state of dipoles in a quasi-one-dimensional ring trap
using few-body techniques combined with analytic arguments. The effective
interaction between two dipoles depends on their center-of-mass coordinate and
can be tuned by varying the angle between dipoles and the plane of the ring.
For weak enough interactions, the state resembles a weakly interacting Fermi
gas or an (inhomogeneous) Lieb-Liniger gas. A mapping between the Lieb-Liniger
and the dipolar-gas parameters in and beyond the Born approximation is
established, and we discuss the effect of inhomogeneities based on a
local-density approximation. For strongly repulsive interactions, the system
exhibits crystal-like localization of the particles. Their inhomogeneous
distribution may be understood in terms of a simple few-body model as well as a
local-density approximation. In the case of partially attractive interactions,
clustered states form for strong enough coupling, and the dependence of the
state on particle number and orientation angle of the dipoles is discussed
analytically.Comment: 15 pages, 10 figure
