# Phase diagram of the Potts model in an applied field

## Abstract

We use the technique of large-q expansion to investigate the phase diagram of the q-state Potts model in an applied field favoring order in one state. The method is valid for any number of dimensions. We find that for q>q/sub C/ (d) there is a first-order phase boundary starting at the zero-field transition point and terminating in a critical point in the interior of the hT plane. Using Pade approximants we obtain for d = 2 the shape and location of this line for various values of q. We also develop a lattice-gas expansion for any d which enables us, in the limit of large but finite q, to map the problem into an equivalent Ising expansion and thus find the exact location and nature of the critical point in this limit.

- Authors:

- Publication Date:

- Research Org.:
- Department of Physics, Brown University, Providence, Rhode Island 02912

- OSTI Identifier:
- 6209728

- DOE Contract Number:
- DE-AC02-76ER03130.A006

- Resource Type:
- Journal Article

- Journal Name:
- Phys. Rev. B: Condens. Matter; (United States)

- Additional Journal Information:
- Journal Volume: 24:3

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ISING MODEL; PHASE DIAGRAMS; MAGNETIC FIELDS; PADE APPROXIMATION; PHASE TRANSFORMATIONS; STATISTICAL MECHANICS; CRYSTAL MODELS; DIAGRAMS; MATHEMATICAL MODELS; MECHANICS; 656000* - Condensed Matter Physics

### Citation Formats

```
Goldschmidt, Y Y.
```*Phase diagram of the Potts model in an applied field*. United States: N. p., 1981.
Web. doi:10.1103/PhysRevB.24.1374.

```
Goldschmidt, Y Y.
```*Phase diagram of the Potts model in an applied field*. United States. https://doi.org/10.1103/PhysRevB.24.1374

```
Goldschmidt, Y Y. Sat .
"Phase diagram of the Potts model in an applied field". United States. https://doi.org/10.1103/PhysRevB.24.1374.
```

```
@article{osti_6209728,
```

title = {Phase diagram of the Potts model in an applied field},

author = {Goldschmidt, Y Y},

abstractNote = {We use the technique of large-q expansion to investigate the phase diagram of the q-state Potts model in an applied field favoring order in one state. The method is valid for any number of dimensions. We find that for q>q/sub C/ (d) there is a first-order phase boundary starting at the zero-field transition point and terminating in a critical point in the interior of the hT plane. Using Pade approximants we obtain for d = 2 the shape and location of this line for various values of q. We also develop a lattice-gas expansion for any d which enables us, in the limit of large but finite q, to map the problem into an equivalent Ising expansion and thus find the exact location and nature of the critical point in this limit.},

doi = {10.1103/PhysRevB.24.1374},

url = {https://www.osti.gov/biblio/6209728},
journal = {Phys. Rev. B: Condens. Matter; (United States)},

number = ,

volume = 24:3,

place = {United States},

year = {1981},

month = {8}

}

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