In statistical mechanics, the ice-type models or six-vertex models are a family of vertex models for crystal lattices with hydrogen bonds. The first such model was introduced by Linus Pauling in 1935 to account for the residual entropy of water ice.[1] Variants have been proposed as models of certain ferroelectric[2] and antiferroelectric[3] crystals.
In 1967, Elliott H. Lieb found the exact solution to a two-dimensional ice model known as "square ice".[4] The exact solution in three dimensions is only known for a special "frozen" state.[5]
- ^ Pauling, L. (1935). "The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement". Journal of the American Chemical Society. 57 (12): 2680–2684. doi:10.1021/ja01315a102.
- ^ Slater, J. C. (1941). "Theory of the Transition in KH2PO4". Journal of Chemical Physics. 9 (1): 16–33. Bibcode:1941JChPh...9...16S. doi:10.1063/1.1750821.
- ^ Rys, F. (1963). "Über ein zweidimensionales klassisches Konfigurationsmodell". Helvetica Physica Acta. 36: 537.
- ^ Lieb, E. H. (1967). "Residual Entropy of Square Ice". Physical Review. 162 (1): 162–172. Bibcode:1967PhRv..162..162L. doi:10.1103/PhysRev.162.162.
- ^ Nagle, J. F. (1969). "Proof of the first order phase transition in the Slater KDP model". Communications in Mathematical Physics. 13 (1): 62–67. Bibcode:1969CMaPh..13...62N. doi:10.1007/BF01645270. S2CID 122432926.
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