### Abstract

We consider two fully frustrated Ising models: the antiferromagnetic triangular model in a field of strength h = HTk_{B}, as well as the Villain model on the square lattice. After a quench from a disordered initial state to T = 0 we study the nonequilibrium dynamics of both models by Monte Carlo simulations. In a finite system of linear size, L, we define and measure sample-dependent 'first passage time', t_{r}, which is the number of Monte Carlo steps until the energy is relaxed to the ground state value. The distribution of t_{r}, in particular its mean value, 〈t _{r}(L)〉, is shown to obey the scaling relation, 〈t _{r}(L)〉∼L^{2}ln(L/L_{0}), for both models. Scaling of the autocorrelation function of the antiferromagnetic triangular model is shown to involve logarithmic corrections, both at H = 0 and at the field-induced Kosterlitz-Thouless transition: however, the autocorrelation exponent is found to be H-dependent.

Original language | English |
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Article number | P07044 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2009 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2009 |

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### Keywords

- Classical Monte Carlo simulations
- Coarsening processes (theory)
- Correlation functions (theory)
- Critical exponents and amplitudes (theory)

### ASJC Scopus subject areas

- Statistics and Probability
- Statistical and Nonlinear Physics
- Statistics, Probability and Uncertainty

### Cite this

*Journal of Statistical Mechanics: Theory and Experiment*,

*2009*(7), [P07044]. https://doi.org/10.1088/1742-5468/2009/07/P07044

**Nonequilibrium dynamics of fully frustrated Ising models at T = 0.** / Karsai, M.; Anglès D'Auriac, J. Ch; Iglói, F.

Research output: Contribution to journal › Article

*Journal of Statistical Mechanics: Theory and Experiment*, vol. 2009, no. 7, P07044. https://doi.org/10.1088/1742-5468/2009/07/P07044

}

TY - JOUR

T1 - Nonequilibrium dynamics of fully frustrated Ising models at T = 0

AU - Karsai, M.

AU - Anglès D'Auriac, J. Ch

AU - Iglói, F.

PY - 2009

Y1 - 2009

N2 - We consider two fully frustrated Ising models: the antiferromagnetic triangular model in a field of strength h = HTkB, as well as the Villain model on the square lattice. After a quench from a disordered initial state to T = 0 we study the nonequilibrium dynamics of both models by Monte Carlo simulations. In a finite system of linear size, L, we define and measure sample-dependent 'first passage time', tr, which is the number of Monte Carlo steps until the energy is relaxed to the ground state value. The distribution of tr, in particular its mean value, 〈t r(L)〉, is shown to obey the scaling relation, 〈t r(L)〉∼L2ln(L/L0), for both models. Scaling of the autocorrelation function of the antiferromagnetic triangular model is shown to involve logarithmic corrections, both at H = 0 and at the field-induced Kosterlitz-Thouless transition: however, the autocorrelation exponent is found to be H-dependent.

AB - We consider two fully frustrated Ising models: the antiferromagnetic triangular model in a field of strength h = HTkB, as well as the Villain model on the square lattice. After a quench from a disordered initial state to T = 0 we study the nonequilibrium dynamics of both models by Monte Carlo simulations. In a finite system of linear size, L, we define and measure sample-dependent 'first passage time', tr, which is the number of Monte Carlo steps until the energy is relaxed to the ground state value. The distribution of tr, in particular its mean value, 〈t r(L)〉, is shown to obey the scaling relation, 〈t r(L)〉∼L2ln(L/L0), for both models. Scaling of the autocorrelation function of the antiferromagnetic triangular model is shown to involve logarithmic corrections, both at H = 0 and at the field-induced Kosterlitz-Thouless transition: however, the autocorrelation exponent is found to be H-dependent.

KW - Classical Monte Carlo simulations

KW - Coarsening processes (theory)

KW - Correlation functions (theory)

KW - Critical exponents and amplitudes (theory)

UR - http://www.scopus.com/inward/record.url?scp=70449431378&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70449431378&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2009/07/P07044

DO - 10.1088/1742-5468/2009/07/P07044

M3 - Article

AN - SCOPUS:70449431378

VL - 2009

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 7

M1 - P07044

ER -