 One aims to calculate the partition function formula_8 of an ice-type model, which is given by the formula

where the sum is taken over all states of the model, formula_1 is the energy of the state, formula_11 is Boltzmann's constant, and formula_12 is the system's temperature.Typically, one is interested in the thermodynamic limit in which the number formula_13 of vertices approaches infinity.In that case, one instead evaluates the free energy per vertex formula_14 in the limit as formula_15, where formula_14 is given by

Equivalently, one evaluates the partition function per vertex formula_18 in the thermodynamic limit, where

The values formula_14 and formula_18 are related by

Several real crystals with hydrogen bonds satisfy the ice model, including ice and potassium dihydrogen phosphate (KDP).