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Finite-size scaling properties of the damage distance and dynamical critical exponent for the Ising model

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  • Wang, Fugao
  • Suzuki, Masuo

Abstract

With the damage spreading method, scaling properties of the damage distance on the Ising model with heat bath dynamics are studied numerically. With the parallel flipping scheme, the scaling curves fall on two curves, which depend on the odd or even lattice sizes. The both scaling curves give the consistent dynamical exponent as z = 2.16±0.04 for d = 2 and z = 2.09±0.05 for d = 3, respectively. By shifting one of them, two curves overlap each other perfectly. Meanwhile, all the scaling curves obtained by single-spin flipping processes (with different odd or even lattice sizes) fall on a single curve, from which the consistent dynamical critical exponent with the parallel scheme is obtained z = 2.18±0.02 for d = 2 and z = 2.08±0.04 for d = 3.

Suggested Citation

  • Wang, Fugao & Suzuki, Masuo, 1995. "Finite-size scaling properties of the damage distance and dynamical critical exponent for the Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 220(3), pages 534-541.
    • Handle: RePEc:eee:phsmap:v:220:y:1995:i:3:p:534-541
    DOI: 10.1016/0378-4371(95)00263-7
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    References listed on IDEAS

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    1. Grassberger, Peter, 1995. "Damage spreading and critical exponents for “model A” Ising dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 214(4), pages 547-559.
    2. Giancarlo Gandolfo & Pier Carlo Padoan & Giuseppe De Arcangelis & Clifford R. Wymer, 1994. "The Italian Continuous Time Model: Results of the Nonlinear Estimation," CESifo Working Paper Series 69, CESifo.
    3. Suzuki, Masuo, 1977. "Scaling theory of fluctuation in superradiance relaxation from the complete inversion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 86(3), pages 622-628.
    4. Jan, Naeem & Stauffer, Dietrich, 1993. "Growth and decay of critical Ising clusters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 199(3), pages 447-452.
    5. Suzuki, Mitsunao, 1969. "金融政策の有効性 : W. L. スミスの批判的検討 = On the Effectiveness of Monetary Policy," 商学討究 (Shogaku Tokyu), Otaru University of Commerce, vol. 20(1), pages 29-46.
    Full references (including those not matched with items on IDEAS)

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