# On the nature of a supposed water model

## Abstract

A cell model that has been proposed by Stanley and Franzese in 2002 for modeling water is based on Potts variables that represent the possible orientations of bonds between water molecules. We show that in the liquid phase, where all cells are occupied by a molecule, the Hamiltonian of the cell model can be rewritten as a Hamiltonian of a conventional Potts model, albeit with two types of coupling constants. We argue that such a model, while having a first-order phase transition, cannot display the critical end point that is postulated for the phase transition between a high- and low-density liquid. A closer look at the mean-field calculations that claim to find such an end point in the cell model reveals that the mean-field theory is constructed such that the symmetry constraints on the order parameter are violated. This is equivalent to introducing an external field. The introduction of such a field can be given a physical justification due to the fact that water does not have the type of long-range order occurring in the Potts model.

- Authors:

- Institut für Festkörperphysik, Technische Universität Darmstadt, Hochschulstr. 6, 64289 Darmstadt (Germany)

- Publication Date:

- OSTI Identifier:
- 22299791

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Advances; Journal Volume: 4; Journal Issue: 8; Other Information: (c) 2014 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; COUPLING CONSTANTS; DENSITY; HAMILTONIANS; LIQUIDS; MEAN-FIELD THEORY; ORDER PARAMETERS; PHASE TRANSFORMATIONS; SIMULATION; WATER

### Citation Formats

```
Heckmann, Lotta, E-mail: lotta@fkp.tu-darmstadt.de, and Drossel, Barbara.
```*On the nature of a supposed water model*. United States: N. p., 2014.
Web. doi:10.1063/1.4892523.

```
Heckmann, Lotta, E-mail: lotta@fkp.tu-darmstadt.de, & Drossel, Barbara.
```*On the nature of a supposed water model*. United States. doi:10.1063/1.4892523.

```
Heckmann, Lotta, E-mail: lotta@fkp.tu-darmstadt.de, and Drossel, Barbara. Fri .
"On the nature of a supposed water model". United States.
doi:10.1063/1.4892523.
```

```
@article{osti_22299791,
```

title = {On the nature of a supposed water model},

author = {Heckmann, Lotta, E-mail: lotta@fkp.tu-darmstadt.de and Drossel, Barbara},

abstractNote = {A cell model that has been proposed by Stanley and Franzese in 2002 for modeling water is based on Potts variables that represent the possible orientations of bonds between water molecules. We show that in the liquid phase, where all cells are occupied by a molecule, the Hamiltonian of the cell model can be rewritten as a Hamiltonian of a conventional Potts model, albeit with two types of coupling constants. We argue that such a model, while having a first-order phase transition, cannot display the critical end point that is postulated for the phase transition between a high- and low-density liquid. A closer look at the mean-field calculations that claim to find such an end point in the cell model reveals that the mean-field theory is constructed such that the symmetry constraints on the order parameter are violated. This is equivalent to introducing an external field. The introduction of such a field can be given a physical justification due to the fact that water does not have the type of long-range order occurring in the Potts model.},

doi = {10.1063/1.4892523},

journal = {AIP Advances},

number = 8,

volume = 4,

place = {United States},

year = {Fri Aug 15 00:00:00 EDT 2014},

month = {Fri Aug 15 00:00:00 EDT 2014}

}