# Disorder-free spin glass transitions and jamming in exactly solvable mean-field models

## TL;DR

This paper introduces exactly solvable mean-field models of vector spins that exhibit glass transitions and jamming without quenched disorder, unifying various phenomena in glassy systems with rotational degrees of freedom.

## Contribution

It develops a mean-field theoretical framework for glass transitions and jamming in vector spin systems with self-generated disorder, applicable to diverse physical contexts.

## Key findings

- Demonstrates self-generated randomness in vector spin models.
- Shows glass transitions involve replica symmetry breaking.
- Links jamming criticality to hard-sphere behavior.

## Abstract

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/non-linear potentials. The existence of self-generated 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 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, continuous the criticality of the jamming or SAT/UNSTAT transition becomes the same as that of hardspheres.