### Abstract

Using a Wang–Landau entropic sampling scheme, we investigate the effects of quenched bond randomness on a particular case of a triangular Ising model with nearest- (Jnn) and next-nearest-neighbor (Jnnn) antiferromagnetic interactions. We consider the case R=Jnnn/Jnn=1, for which the pure model is known to have a columnar ground state where rows of nearest-neighbor spins up and down alternate and undergo a weak first-order phase transition from the ordered to the paramagnetic state. With the introduction of quenched bond randomness we observe the effects signaling the expected conversion of the first-order phase transition to a second-order phase transition and using the Lee–Kosterlitz method, we quantitatively verify this conversion. The emerging, under random bonds, continuous transition shows a strongly saturating specific heat behavior, corresponding to a negative exponent α, and belongs to a new distinctive universality class with ν=1.135(11), γ/ν=1.744(9), and β/ν=0.124(8). Thus, our results for the critical exponents support an extensive but weak universality and the emerged continuous transition has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of two-dimensional (2d) systems without and with quenched disorder.

Original language | English |
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Pages (from-to) | 4950–4958 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 388 |

Issue number | 24 |

DOIs | |

Publication status | Published - 22 Aug 2009 |

### Bibliographical note

The full text is currently unavailable on the repository.### Keywords

- Quenched bond randomness
- Weak universality
- First-order transitions
- Triangular Ising model
- superantiferromagnetism
- Entropic sampling

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## Cite this

Fytas, N. G., & Malakis, A. (2009). Criticality in the randomness-induced second-order phase transition of the triangular Ising antiferromagnet with nearest- and next-nearest-neighbor interactions.

*Physica A: Statistical Mechanics and its Applications*,*388*(24), 4950–4958. https://doi.org/10.1016/j.physa.2009.08.022