We discuss a possible mechanism leading to localisation of the low-lying
Dirac eigenmodes in high-temperature lattice QCD, based on the spatial
fluctuations of the local Polyakov lines in the partially ordered
configurations above $T_c$. This mechanism provides a qualitative explanation
of the dependence of localisation on the temperature and on the lattice
spacing, and also of the phase diagram of QCD with an imaginary chemical
potential. To test the viability of this mechanism we propose a
three-dimensional effective, Anderson-like model, mimicking the effect of the
Polyakov lines on the quarks. The diagonal, on-site disorder is governed by a
three-dimensional Ising-like spin model with continuous spins. Our numerical
results show that localised modes are indeed present in the ordered phase of
the Ising model, thus supporting the proposed mechanism for localisation in
QCD.Comment: 20 pages, 5 figure