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arXiv:cond-mat/0107509 · Physica A Statistical Mechanics and its Applications

Autocorrelation functions in 3D fully frustrated systems

Giancarlo Franzese, Annalisa Fierro, ANTONIO DE CANDIA, Antonio Coniglio A

Published Aug 1, 1998• 3 citations
arXivHTMLPDF
DOI
10.1016/s0378-4371(98)00162-9

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We study the aging of the two-dimensional fully-frustrated Ising and threestate Potts models by means of Monte Carlo simulations. The system is initially prepared at infinite temperature and then quenched either at its critical temperature or in the low-temperature phase for the three-state Potts model. Autocorrelation and response functions are shown to satisfy the scaling behavior conjectured for aging ferromagnets if one assumes the existence of logarithmic corrections. The dynamical and autocorrelation exponents are compatible with � = d and z = 2 for the Ising model and probably the threestate Potts model both at and below Tc. The fluctuation-dissipation ratio goes asymptotically to different non-trivial values at Tc and does not vanish below Tc.
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.