We describe why Ising spin chains with competing interactions in SrHo2βO4β segregate into ordered and disordered ensembles at low temperatures
(T). Using elastic neutron scattering, magnetization, and specific heat
measurements, the two distinct spin chains are inferred to have N\'eel
(ββββ) and double-N\'eel
(ββββ) ground states respectively. Below
TNβ=0.68(2)~K, the N\'eel chains develop three dimensional (3D) long
range order (LRO), which arrests further thermal equilibration of the
double-N\'eel chains so they remain in a disordered incommensurate state for
T below TSβ=0.52(2)~K. SrHo2βO4β distills an important
feature of incommensurate low dimensional magnetism: kinetically trapped
topological defects in a quasiβdβdimensional spin system can preclude order
in d+1 dimensions.Comment: 10 pages, 10 figure