  The hallmark of highly frustrated systems is the presence of many states
close in energy to the ground state. Fluctuations between these states can
preclude the emergence of any form of order and lead to the appearance of spin
liquids. Even on the classical level, spin liquids are not all alike: they may
have algebraic or exponential correlation decay, and various forms of long
wavelength description, including vector or tensor gauge theories. Here, we
introduce a classification scheme, allowing us to fit the diversity of
classical spin liquids (CSLs) into a general framework as well as predict and
construct new kinds. CSLs with either algebraic or exponential
correlation-decay can be classified via the properties of the bottom flat
band(s) in their soft-spin Hamiltonians. The classification of the former is
based on the algebraic structures of gapless points in the spectra, which
relate directly to the emergent generalized Gauss's laws that control the low
temperature physics. The second category of CSLs, meanwhile, are classified by
the fragile topology of the gapped bottom band(s). Utilizing the classification
scheme we construct new models realizing exotic CSLs, including one with
anisotropic generalized Gauss's laws and charges with subdimensional mobility,
one with a network of pinch-line singularities in its correlation functions,
and a series of fragile topological CSLs connected by zero-temperature
transitions.
