  Fractons are topological quasiparticles with limited mobility. While there
exists a variety of models hosting these excitations, typical fracton systems
require rather complicated many-particle interactions. Here, we discuss fracton
behavior in the more common physical setting of classical kagome spin models
with frustrated two-body interactions only. We investigate systems with
different types of elementary spin degrees of freedom (three-state Potts, XY,
and Heisenberg spins) which all exhibit characteristic subsystem symmetries and
fracton-like excitations. The mobility constraints of isolated fractons and
bound fracton pairs in the three-state Potts model are, however, strikingly
different compared to the known type-I or type-II fracton models. One may still
explain these properties in terms of type-I fracton behavior and construct an
effective low-energy tensor gauge theory when considering the system as a 2D
cut of a 3D cubic lattice model. Our extensive classical Monte-Carlo
simulations further indicate a crossover into a low temperature glassy phase
where the system gets trapped in metastable fracton states. Moving on to XY
spins, we find that in addition to fractons the system hosts fractional vortex
excitations. As a result of the restricted mobility of both types of defects,
our classical Monte-Carlo simulations do not indicate a Kosterlitz-Thouless
transition but again show a crossover into a glassy low-temperature regime.
Finally, the energy barriers associated with fractons vanish in the case of
Heisenberg spins, such that defect states may continuously decay into a ground
state. These decays, however, exhibit a power-law relaxation behavior which
leads to slow equilibration dynamics at low temperatures.
