The challenge of understanding phase transitions and proton ordering in hydrogen-bonded ferroelectrics (such as KDP, squaric acid, croconic acid) and different crystal phases of ice has been a rich source of lattice models for statistical physics.
Models include ice-type models (six-vertex model, Slater's KDP model), transverse field Ising model, and some gauge theories. Some of the classical (quantum) models are exactly soluble in two (one) dimensions.
An important question that seems to be skimmed over is the following: under what assumptions can one actually "derive" these models starting from the actual crystal structure and electronic and vibrational properties of a specific material?
That quantum effects, particularly tunnelling of protons, are important in some of the materials is indicated by the large shifts (of the order of 100 percent) seen in the transition temperatures upon H/D isotope substitution.
In 1963 de Gennes argued that the transverse field Ising model should describe the collective excitations of protons tunnelling between different molecular units in an H-bonded ferroelectric. Some of this is discussed in detail in an extensive review by Blinc and Zeks.
An important issue is whether the phase transition is an "order-disorder" transition or a "displacive" transition. I think what this means is the following. In the former case, the transition is driven by the pseudo-spin variables and there is no soft lattice mode associated with the transition.
Perhaps, in different language, is it appropriate to "integrate out" the vibrational degrees of freedom?
[Aside: this reminds me of some issues that I looked at in a Holstein model about 20 years ago].
There are a lot of papers that make quantitative comparisons between experimental properties and the predictions of a transverse field Ising model (usually treated in the mean-field approximation).
One example (which also highlights the role of isotope effects) is
Quantum phase transition in K3D1−xHx(SO4)2
Y. Moritomo, Y. Tokura, N. Nagaosa, T. Suzuki, and K. Kumagai
One problem I am puzzling over is that the model parameters that they (and others) extract are different from what I would expect from knowing the actual bond lengths, vibrational frequencies, in the system and the energetics of different H-bond states. I can only "derive" pseudo-spin models with quite restrictive assumptions.
A recent paper that looks some of rich physics associated with collective quantum effects is
Classical and quantum theories of proton disorder in hexagonal water ice
Owen Benton, Olga Sikora, and Nic Shannon