5 N ov 2 00 1 Scaling Exponent for Coarsening in a 1 D q - state system
نویسنده
چکیده
An exponent β which characterises non-equilibrium coarsening processes is calculated in a deterministic solvable model of coarsening for a 1D q-state Potts system. We study how the fraction of sites P which have never changed their state, scale with the characteristic domain length 〈l〉. β is defined by P ∼ 〈l〉β−1. We propose a new model of coarsening that prevents correlations from developing between domains thereby ensuring tractability and an exact result for any q. PACS: 02.50,05.20
منابع مشابه
N ov 2 00 1 Scaling Exponent for Coarsening in a 1 D q - state system
An exponent β which characterises non-equilibrium coarsening processes is calculated in a deterministic solvable model of coarsening for a 1D q-state Potts system. We study how the fraction of sites P which have never changed their state, scale with the characteristic domain length 〈l〉. β is defined by P ∼ 〈l〉β−1. We propose a new model of coarsening that prevents correlations from developing b...
متن کاملar X iv : c on d - m at / 9 51 10 40 v 1 8 N ov 1 99 5 Coarsening and Persistence in the Voter Model
We investigate coarsening and persistence in the voter model by introducing the quantity Pn(t), defined as the fraction of voters who changed their opinion n times up to time t. We show that Pn(t) exhibits scaling behavior that strongly depends on the dimension as well as on the initial opinion concentrations. Exact results are obtained for the average number of opinion changes, 〈n〉, and the au...
متن کاملScaling Behavior of Response Functions in the Coarsening Dynamics of Disordered Ferromagnets
We study coarsening dynamics in the ferromagnetic random bond Ising model in d = 1, 2. We focus on the validity of super-universality and the scaling properties of the response functions. In the d = 1 case, we obtain a complete understanding of the evolution, from preasymptotic to asymptotic behavior. The corresponding response function shows a clear violation of super-universality. Further, ou...
متن کاملar X iv : a da p - or g / 99 11 00 4 v 1 1 9 N ov 1 99 9 Criticality and Punctuated Equilibrium in a Spin System Model of a Financial Market
We describe a financial market model which shows a non-equilibrium phase transition. Near the transition punctuated equilibrium behaviour is seen, with avalanches occuring on all scales. This scaling is described by an exponent very near 1. This system shows intermittent time development with bursts of global synchronization reminiscent of a market rollercoaster.
متن کاملar X iv : q ua nt - p h / 05 11 05 9 v 1 7 N ov 2 00 5 Phase Sensitivity of a Mach -
The best performance of a Mach-Zehnder interferometer is achieved with the input state |NT /2+ 1〉|NT /2 − 1〉 + |NT /2 − 1〉|NT /2 + 1〉, being NT the total number of atoms/photons. This gives: i) a phase-shift error confidence C68% = 2.67/NT with ii) a single interferometric measurement. Different input quantum states can achieve the Heisenberg scaling ∼ 1/NT but with higher prefactors and at the...
متن کامل