Nonequilibrium dynamics of fully frustrated Ising models at T = 0

M. Karsai; J. Ch Anglès D'Auriac; F. Iglói

doi:10.48550/arXiv.0905.3503

Nonequilibrium dynamics of fully frustrated Ising models at T = 0

M. Karsai^*, J. Ch Anglès D'Auriac, F. Iglói

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract (may include machine translation)

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)〉∼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.

Original language	English
Article number	P07044
Journal	Journal of Statistical Mechanics: Theory and Experiment
Volume	2009
Issue number	7
DOIs	https://doi.org/10.48550/arXiv.0905.3503 https://doi.org/10.1088/1742-5468/2009/07/P07044
State	Published - 2009
Externally published	Yes

Keywords

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

Access to Document

Cite this

@article{75fa55c91f174d3880327dc28dce204b,

title = "Nonequilibrium dynamics of fully frustrated Ising models at T = 0",

abstract = "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.",

keywords = "Classical Monte Carlo simulations, Coarsening processes (theory), Correlation functions (theory), Critical exponents and amplitudes (theory)",

author = "M. Karsai and {Angl{\`e}s D'Auriac}, {J. Ch} and F. Igl{\'o}i",

year = "2009",

doi = "10.48550/arXiv.0905.3503",

language = "English",

volume = "2009",

journal = "Journal of Statistical Mechanics: Theory and Experiment",

issn = "1742-5468",

number = "7",

}

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

U2 - 10.48550/arXiv.0905.3503

DO - 10.48550/arXiv.0905.3503

M3 - Article

AN - SCOPUS:70449431378

SN - 1742-5468

VL - 2009

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

IS - 7

M1 - P07044

ER -

Nonequilibrium dynamics of fully frustrated Ising models at T = 0

Abstract (may include machine translation)

Keywords

Access to Document

Other files and links

Fingerprint

Cite this