  Higher-order nodal line semimetals represent a recently proposed topological
semimetal class that harbors bulk nodal lines and features gapless hinge Fermi
arc excitations, governed by the bulk-hinge correspondence. In this study, we
investigate the disorder effect on a higher-order nodal line semimetal and the
consequent phase transitions. Within the pristine higher-order nodal line
semimetal model, we unveil three distinct phases: higher-order nodal line
semimetal, conventional nodal line semimetal, and normal insulator. The
higher-order nodal line semimetal is characterized by one-dimensional hinge
Fermi arc states connecting a pair of nodal rings, contrasting with
conventional nodal line semimetals that exhibit two-dimensional drumhead
surface states. We demonstrate that disorder can trigger multiple phase
transitions within this system. Significantly, intermediate disorder can induce
higher-order topology in an initial conventional nodal line semimetal or even
an initial normal insulator. Further increase in disorder drives the system
through a diffusive metallic phase before ultimately reaching the Anderson
insulator regime. Employing a combination of finite-size scaling analysis and
an effective medium theory, we construct a comprehensive phase diagram,
elucidating the intricate interplay between disorder and topology.
