Compare the Hamiltonian of equation 8.1 to the Hamiltonian of section 6.2 where the classical Ising model was described. There the dimensionality of the spins was taken to be one, and the dimensionality of the space that the spins are ordered within was taken to be one. The coupling parameter 
was taken constant for nearest neighbors and zero for non-nearest neighbors, and the external field 
was taken constant for all spins. The common usage is to name the models after the dimensionality of the spins regardless of the spatial dimension. Thus, one dimensional spins organized in any way spatially with whatever coupling strengths are denoted by the term Ising model. When the dimensionality of the spins is three, the coupled spin system is called the Heisenberg model.
In general, the spin-spin coupling may be anisotropic or isotropic, both in the space and the spin dimensions. The spin-spin coupling can be nearest neighbor, farther than nearest neighbor, etc. We can also consider either a zero or a nonzero external field, , which may be coupled either isotropically or anisotropically in the space and spin dimensions.
Another detail that arises is whether or not the spins have a fixed size. There are so-called soft spin models, where the spins are allowed to have any size, but the Hamiltonian for these soft-spin models is generally taken to be different from that of equation 8.1. See [24] for further details.
There is also the relevant detail of whether an equilibrium solution to any particular model system has been found, and what the properties of the solution are - does it demonstrate a phase transition, etc. The form of the mean field theory solution is also of interest.
There is no compilation of the various systems that have been considered, and new solutions are regularly being found. In summary, we may categorize by spin and space dimensions, known solutions and properties of the solutions (classical or quantum, in mean field, nonzero or zero external field, isotropic or anisotropic spin-spin coupling in space and spin dimensions, isotropic or anisotropic field-spin coupling in space and spin dimensions, and whether the solution demonstrates interesting properties, such as phase transitions, etc.). For classical spin models the interested reader may consult [6, 7, 83, 30] Classical spin glasses are discussed in [10, 24, 60]. For quantum spin models the reader may consult [86, 44, 89, 64, 1, 70, 82, 56] among others. In all cases no reduced distributions are considered, and no reduced entropies or information correlation functions are considered. [89] is a good example of a numerical paper treating the two-dimensional quantum Heisenberg spin-1/2 model with exchange and dipole interactions. At the time of preparing the final draft of this document the authors of [13] (Los Alamos) indicated that they had heard rumors of a collaboration which was approaching the solution of the long-range quantum Heisenberg model using the results of [13]. A result like this would be useful in finding the complete time-evolution solution of the model.