  The generalized mean-field orthoplicial model is a mean-field model on a
space of continuous spins on $\mathbb{R}^n$ that are constrained to a scaled
$(n-1)$-dimensional $\ell_1$-sphere, equivalently a scaled $(n-1)$-dimensional
orthoplex, and interact through a general interaction function. The finite
volume Gibbs states of this model correspond to singular probability measures.
In this paper, we use probabilistic methods to rigorously classify the infinite
volume Gibbs states of this model, and we show that they are convex
combinations of product states. The predominant methods utilize the theory of
large deviations, relative entropy, and equivalence of ensembles, and the key
technical tools utilize exact integral representations of certain partition
functions and locally uniform estimates of expectations of certain local
observables.
