We construct and analyze a family of MM-component
vectorial spin systems which exhibit glass transitions and jamming
within supercooled paramagnetic states without quenched disorder. Our
system is defined on lattices with connectivity
c=\alpha Mc=αM
and becomes exactly solvable in the limit of large number of components
M \to \inftyM→∞.
We consider generic pp-body
interactions between the vectorial Ising/continuous spins with
linear/non-linear potentials. The existence of self-generated randomness
is demonstrated by showing that the random energy model is recovered
from a MM-component
ferromagnetic pp-spin
Ising model in M \to \inftyM→∞
and p \to \inftyp→∞
limit. In our systems the quenched disorder, if present, and the
self-generated disorder act additively. Our theory provides a unified
mean-field theoretical framework for glass transitions of rotational
degree of freedoms such as orientation of molecules in glass forming
liquids, color angles in continuous coloring of graphs and vector spins
of geometrically frustrated magnets. The rotational glass transitions
accompany various types of replica symmetry breaking. In the case of
repulsive hardcore interactions in the spin space, the criticality of
the jamming or SAT/UNSTAT transition becomes the same as that of
hardspheres.
The de Almeida–Thouless Line in Hierarchical Quantum Spin Glasses
