  Magnetic frustration and low dimensionality can prevent long range magnetic
order and lead to exotic correlated ground states. SrDy$_2$O$_4$ consists of
magnetic Dy$^{3+}$ ions forming magnetically frustrated zig-zag chains along
the c-axis and shows no long range order to temperatures as low as $T=60$ mK.
We carried out neutron scattering and AC magnetic susceptibility measurements
using powder and single crystals of SrDy$_2$O$_4$. Diffuse neutron scattering
indicates strong one-dimensional (1D) magnetic correlations along the chain
direction that can be qualitatively accounted for by the axial next-nearest
neighbour Ising (ANNNI) model with nearest-neighbor and next-nearest-neighbor
exchange $J_1=0.3$ meV and $J_2=0.2$ meV, respectively. Three-dimensional (3D)
correlations become important below $T^*\approx0.7$ K. At $T=60$ mK, the short
range correlations are characterized by a putative propagation vector
$\textbf{k}_{1/2}=(0,\frac{1}{2},\frac{1}{2})$. We argue that the absence of
long range order arises from the presence of slowly decaying 1D domain walls
that are trapped due to 3D correlations. This stabilizes a low-temperature
phase without long range magnetic order, but with well-ordered chain segments
separated by slowly-moving domain walls.
