2013
DOI: 10.1007/s10955-013-0757-1
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Drift of Phase Fluctuations in the ABC Model

Abstract: In a recent work, Bodineau and Derrida analyzed the phase fluctuations in the ABC model. In particular, they computed the asymptotic variance and, on the basis of numerical simulations, they conjectured the presence of a drift, which they guessed to be an antisymmetric function of the three densities. By assuming the validity of the fluctuating hydrodynamic approximation, we prove the presence of such a drift, providing an analytical expression for it. This expression is then shown to be an antisymmetric funct… Show more

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Cited by 2 publications
(10 citation statements)
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“…Anomalous coarsening with logarithmic domain growth has been identified in a variety of situations with dynamical constraints, as for example in the ABC model introduced by Evans et al [26,27], where three different particle types swap places asymmetrically, in the model discussed by Lahiri and Ramaswamy [28,29], where two sublattices are considered with two types of particles on each sublattice, or in the driven two-lane particle system studied by Lipowski and Lipowska [30]. Among these models, the one-dimensional ABC model has enjoyed much attention in recent years [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], due to its unique properties combined with its amenability to exact calculations in some special cases. Thus the ABC model provides an opportunity to study exactly the long-range correlations in a system undergoing a non-equilibrium phase transition as well as to elucidate ensemble inequivalence far from equilibrium.…”
Section: Introductionmentioning
confidence: 99%
“…Anomalous coarsening with logarithmic domain growth has been identified in a variety of situations with dynamical constraints, as for example in the ABC model introduced by Evans et al [26,27], where three different particle types swap places asymmetrically, in the model discussed by Lahiri and Ramaswamy [28,29], where two sublattices are considered with two types of particles on each sublattice, or in the driven two-lane particle system studied by Lipowski and Lipowska [30]. Among these models, the one-dimensional ABC model has enjoyed much attention in recent years [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], due to its unique properties combined with its amenability to exact calculations in some special cases. Thus the ABC model provides an opportunity to study exactly the long-range correlations in a system undergoing a non-equilibrium phase transition as well as to elucidate ensemble inequivalence far from equilibrium.…”
Section: Introductionmentioning
confidence: 99%
“…The fact that the leading order contribution to the local correlation function, A i B i+1 C i+2 , is given by the corresponding product of the coarse-grained density profiles is a characteristic property of diffusive systems. It is shown explicitly for the equal-densities ABC model in [28,41] and argued to be true also for arbitrary average densities in [32,41]. The deposition rate is computed in a similar way, yielding…”
Section: B Nonperturbative Study Of the Non-conseving Phase Diagrammentioning
confidence: 88%
“…The density profile is periodic, ρ α (x + 1, τ ) = ρ α (x, τ ), and due to exclusion it obeys ρ 0 (x, τ ) = 1 − α ρ α (x, τ ) ≤ 1. Equation (13) has been shown to be exact in the L → ∞ limit for equal densities and r = 1 [28,41], and has been argued to remain valid even for arbitrary average densities [32,41]. The mapping discussed in Sec.…”
Section: Abc Model With Non-equal Densities and Vanishingly Slowmentioning
confidence: 99%
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