# Phase transitions and critical properties in the antiferromagnetic Ising model on a layered triangular lattice with allowance for intralayer next-nearest-neighbor interactions

## Abstract

The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scaling theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.

- Authors:

- Russian Academy of Sciences, Institute of Physics, Dagestan Scientific Center (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22617166

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Experimental and Theoretical Physics; Journal Volume: 123; Journal Issue: 4; Other Information: Copyright (c) 2016 Pleiades Publishing, Inc.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ALGORITHMS; ANTIFERROMAGNETISM; CORRELATIONS; INTERACTIONS; ISING MODEL; MONTE CARLO METHOD; ORDER PARAMETERS; PARAMAGNETISM; PHASE TRANSFORMATIONS; REPLICAS; SCALING; SPECIFIC HEAT; TRIANGULAR CONFIGURATION

### Citation Formats

```
Badiev, M. K., E-mail: m-zagir@mail.ru, Murtazaev, A. K., and Ramazanov, M. K.
```*Phase transitions and critical properties in the antiferromagnetic Ising model on a layered triangular lattice with allowance for intralayer next-nearest-neighbor interactions*. United States: N. p., 2016.
Web. doi:10.1134/S1063776116090016.

```
Badiev, M. K., E-mail: m-zagir@mail.ru, Murtazaev, A. K., & Ramazanov, M. K.
```*Phase transitions and critical properties in the antiferromagnetic Ising model on a layered triangular lattice with allowance for intralayer next-nearest-neighbor interactions*. United States. doi:10.1134/S1063776116090016.

```
Badiev, M. K., E-mail: m-zagir@mail.ru, Murtazaev, A. K., and Ramazanov, M. K. Sat .
"Phase transitions and critical properties in the antiferromagnetic Ising model on a layered triangular lattice with allowance for intralayer next-nearest-neighbor interactions". United States. doi:10.1134/S1063776116090016.
```

```
@article{osti_22617166,
```

title = {Phase transitions and critical properties in the antiferromagnetic Ising model on a layered triangular lattice with allowance for intralayer next-nearest-neighbor interactions},

author = {Badiev, M. K., E-mail: m-zagir@mail.ru and Murtazaev, A. K. and Ramazanov, M. K.},

abstractNote = {The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scaling theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.},

doi = {10.1134/S1063776116090016},

journal = {Journal of Experimental and Theoretical Physics},

number = 4,

volume = 123,

place = {United States},

year = {Sat Oct 15 00:00:00 EDT 2016},

month = {Sat Oct 15 00:00:00 EDT 2016}

}