Title: Subexponentially growing Hilbert space and nonconcentrating distributions in a constrained spin model,
Abstract: Motivated by recent experiments with two-component Bose-Einstein condensates,
we study fully-connected spin models subject to an additional constraint. The
constraint is responsible for the Hilbert space dimension to scale only
linearly with the system size. We discuss the unconventional statistical
physical and thermodynamic properties of such a system, in particular the
absence of concentration of the underlying probability distributions. As a
consequence, expectation values are less suitable to characterize such systems,
and full distribution functions are required instead. Sharp signatures of phase
transitions do not occur in such a setting, but transitions from singly peaked
to doubly peaked distribution functions of an "order parameter" may be present.