# Tricriticality in crossed Ising chains

## Abstract

We explore the phase diagram of Ising spins on one-dimensional chains which criss-cross in two perpendicular directions and which are connected by interchain couplings. This system is of interest as a simpler, classical analog of a quantum Hamiltonian which has been proposed as a model of magnetic behavior in Nb _{12}O _{29} and also, conceptually, as a geometry which is intermediate between one and two dimensions. Here, using mean field theory as well as Metropolis Monte Carlo and Wang-Landau simulations, we locate quantitatively the boundaries of four ordered phases. Each becomes an effective Ising model with unique effective couplings at large interchain coupling. Away from this limit we demonstrate non-trivial critical behavior, including tricritical points which separate first and second order phase transitions. Finally, we present evidence that this model belongs to the 2D Ising universality class.

- Authors:

- Univ. of California, Davis, CA (United States). Dept. of Physics

- Publication Date:

- Research Org.:
- Univ. of California, Davis, CA (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1477008

- Alternate Identifier(s):
- OSTI ID: 1398736

- Grant/Contract Number:
- SC0014671

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review E

- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 4; Journal ID: ISSN 2470-0045

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

### Citation Formats

```
Cary, T., Singh, R. R. P., and Scalettar, R. T.
```*Tricriticality in crossed Ising chains*. United States: N. p., 2017.
Web. doi:10.1103/PhysRevE.96.042108.

```
Cary, T., Singh, R. R. P., & Scalettar, R. T.
```*Tricriticality in crossed Ising chains*. United States. doi:10.1103/PhysRevE.96.042108.

```
Cary, T., Singh, R. R. P., and Scalettar, R. T. Mon .
"Tricriticality in crossed Ising chains". United States.
doi:10.1103/PhysRevE.96.042108. https://www.osti.gov/servlets/purl/1477008.
```

```
@article{osti_1477008,
```

title = {Tricriticality in crossed Ising chains},

author = {Cary, T. and Singh, R. R. P. and Scalettar, R. T.},

abstractNote = {We explore the phase diagram of Ising spins on one-dimensional chains which criss-cross in two perpendicular directions and which are connected by interchain couplings. This system is of interest as a simpler, classical analog of a quantum Hamiltonian which has been proposed as a model of magnetic behavior in Nb12O29 and also, conceptually, as a geometry which is intermediate between one and two dimensions. Here, using mean field theory as well as Metropolis Monte Carlo and Wang-Landau simulations, we locate quantitatively the boundaries of four ordered phases. Each becomes an effective Ising model with unique effective couplings at large interchain coupling. Away from this limit we demonstrate non-trivial critical behavior, including tricritical points which separate first and second order phase transitions. Finally, we present evidence that this model belongs to the 2D Ising universality class.},

doi = {10.1103/PhysRevE.96.042108},

journal = {Physical Review E},

number = 4,

volume = 96,

place = {United States},

year = {Mon Oct 09 00:00:00 EDT 2017},

month = {Mon Oct 09 00:00:00 EDT 2017}

}