# Ground-state entropy of the Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on strips of the square lattice

## Abstract

We present exact calculations of the zero-temperature partition function (chromatic polynomial) and W(q), the exponent of the ground-state entropy, for the q-state Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on square lattice strips, of width L{sub y}=3 and L{sub y}=4 vertices and arbitrarily great length L{sub x} vertices, with both free and periodic boundary conditions. The resultant values of W for a range of physical q values are compared with each other and with the values for the full two-dimensional lattice. These results give insight into the effect of such nonnearest-neighbor couplings on the ground-state entropy. We show that the q=2 (Ising) and q=4 Potts antiferromagnets have zero-temperature critical points on the L{sub x}{yields}{infinity} limits of the strips that we study. With the generalization of q from Z{sub +} to C, we determine the analytic structure of W(q) in the q plane for the various cases.

- Authors:

- Publication Date:

- Sponsoring Org.:
- (US)

- OSTI Identifier:
- 40205393

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review E

- Additional Journal Information:
- Journal Volume: 62; Journal Issue: 4; Other Information: Othernumber: PLEEE8000062000004004650000001; 034010PRE; PBD: Oct 2000; Journal ID: ISSN 1063-651X

- Publisher:
- The American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY CONDITIONS; ENTROPY; PARTITION FUNCTIONS

### Citation Formats

```
Chang, Shu-Chiuan, and Shrock, Robert.
```*Ground-state entropy of the Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on strips of the square lattice*. United States: N. p., 2000.
Web. doi:10.1103/PhysRevE.62.4650.

```
Chang, Shu-Chiuan, & Shrock, Robert.
```*Ground-state entropy of the Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on strips of the square lattice*. United States. https://doi.org/10.1103/PhysRevE.62.4650

```
Chang, Shu-Chiuan, and Shrock, Robert. Sun .
"Ground-state entropy of the Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on strips of the square lattice". United States. https://doi.org/10.1103/PhysRevE.62.4650.
```

```
@article{osti_40205393,
```

title = {Ground-state entropy of the Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on strips of the square lattice},

author = {Chang, Shu-Chiuan and Shrock, Robert},

abstractNote = {We present exact calculations of the zero-temperature partition function (chromatic polynomial) and W(q), the exponent of the ground-state entropy, for the q-state Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on square lattice strips, of width L{sub y}=3 and L{sub y}=4 vertices and arbitrarily great length L{sub x} vertices, with both free and periodic boundary conditions. The resultant values of W for a range of physical q values are compared with each other and with the values for the full two-dimensional lattice. These results give insight into the effect of such nonnearest-neighbor couplings on the ground-state entropy. We show that the q=2 (Ising) and q=4 Potts antiferromagnets have zero-temperature critical points on the L{sub x}{yields}{infinity} limits of the strips that we study. With the generalization of q from Z{sub +} to C, we determine the analytic structure of W(q) in the q plane for the various cases.},

doi = {10.1103/PhysRevE.62.4650},

url = {https://www.osti.gov/biblio/40205393},
journal = {Physical Review E},

issn = {1063-651X},

number = 4,

volume = 62,

place = {United States},

year = {2000},

month = {10}

}