  A quadratic extension of REM has been treated. Discussed here is the origin
of relation of REM to strings and other complex physical phenomena. Two basic
features of the REM class of complex phenomena were identified: the double
thermodynamic reflection (a hierarchy of free energies) including the strong
reflection at the upper level (the free energy on the order of a logarithm of
the degrees of freedom) and the loss (complete or partial) of the local
symmetry property. Two main classes of complex phenomena related to REM are
seen: the spin glass phase of REM and the boundary the spin glass-ferromagnetic
phases. Some examples of physics interest are analyzed from this viewpoint.
