Nonequilibrium dynamics of fully frustrated Ising models at T = 0

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

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish
Article numberP07044
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2009
Issue number7
DOIs
Publication statusPublished - 2009

Fingerprint

Nonequilibrium Dynamics
Ising model
Ising Model
autocorrelation
Triangular
scaling
Model
Scaling Relations
Dependent
First Passage Time
Autocorrelation Function
Autocorrelation
Square Lattice
Mean Value
Ground State
Logarithmic
Monte Carlo Simulation
Exponent
exponents
Scaling

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

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

In: Journal of Statistical Mechanics: Theory and Experiment, Vol. 2009, No. 7, P07044, 2009.

Research output: Contribution to journalArticle

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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.

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