SciPost Phys. 4, 040 (2018) ·
published 26 June 2018

· pdf
We construct and analyze a family of $M$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 $c=\alpha M$ and becomes exactly solvable in the limit of large
number of components $M \to \infty$. We consider generic $p$body interactions
between the vectorial Ising/continuous spins with linear/nonlinear potentials.
The existence of selfgenerated randomness is demonstrated by showing that the
random energy model is recovered from a $M$component ferromagnetic $p$spin
Ising model in $M \to \infty$ and $p \to \infty$ limit. In our systems the
quenched disorder, if present, and the selfgenerated disorder act additively.
Our theory provides a unified meanfield 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, continuous the
criticality of the jamming or SAT/UNSTAT transition becomes the same as that of
hardspheres.
Submissions
Submissions for which this Contributor is identified as an author:
Prof. Yoshino: "In my response to << report 1>..."
in Submission on From complex to simple : hierarchical freeenergy landscape renormalized in deep neural networks by Hajime Yoshino