Exact Scaling Functions for One-Dimensional Stationary KPZ Growth

Prähofer, Michael; Spohn, Herbert

doi:10.1023/b:joss.0000019810.21828.fc

Cited by 266 publications

(411 citation statements)

References 34 publications

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“…Within the error bars, our data are in reasonable aggreement with the stretched exponential function f (y) ∝ exp(−cy 3 ), where c = 0.295 (5), that was computed in Ref. [25].…”

Section: Scaling Functionssupporting

confidence: 87%

“…whereas equivalently the matching condition b = t −1/z leads to [25] C(x, t) ∝ t 2/3 g(y), y = x/t 2/3 .…”

Section: Scaling Functionsmentioning

confidence: 99%

“…The scaling form of the density-density correlation of the driven lattice gas has been derived and the associated scaling exponents calculated by means of renormalization group techniques [14][15][16]. Scaling functions have been computed by means of the mode-coupling approximation [17][18][19][20][21][22][23], exact numerical integration [24][25][26], and other analytical approaches [27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

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Slow relaxation and aging kinetics for the driven lattice gas

Daquila

Täuber

2011

Phys. Rev. E

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We numerically investigate the long-time behavior of the density-density auto-correlation function in driven lattice gases with particle exclusion and periodic boundary conditions in one, two, and three dimensions using precise Monte Carlo simulations. In the one-dimensional asymmetric exclusion process on a ring with half the lattice sites occupied, we find that correlations induce extremely slow relaxation to the asymptotic power law decay. We compare the crossover functions obtained from our simulations with various analytic results in the literature, and analyze the characteristic oscillations that occur in finite systems away from half-filling. As expected, in three dimensions correlations are weak and consequently the mean-field description is adequate. We also investigate the relaxation towards the nonequilibrium steady state in the two-time density-density auto-correlations, starting from strongly correlated initial conditions. We obtain simple aging scaling behavior in one, two, and three dimensions, with the expected power laws.

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“…Within the error bars, our data are in reasonable aggreement with the stretched exponential function f (y) ∝ exp(−cy 3 ), where c = 0.295 (5), that was computed in Ref. [25].…”

Section: Scaling Functionssupporting

confidence: 87%

“…whereas equivalently the matching condition b = t −1/z leads to [25] C(x, t) ∝ t 2/3 g(y), y = x/t 2/3 .…”

Section: Scaling Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Slow relaxation and aging kinetics for the driven lattice gas

Daquila

Täuber

2011

Phys. Rev. E

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“…In the picture of the directed polymer, it chooses either one of the two boundaries and the fluctuations from the boundary portions are comparable in size to the ones coming from the bulk. Such fluctuation properties are studied for PNG in [39] and for the TASEP in [16].…”

Section: Boundary Sourcesmentioning

confidence: 99%

Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals

Spohn

2006

Physica A: Statistical Mechanics and its Applications

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111

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Three models from statistical physics can be analyzed by employing space-time determinantal processes: (1) crystal facets, in particular the statistical properties of the facet edge, and equivalently tilings of the plane, (2) one-dimensional growth processes in the Kardar-Parisi-Zhang universality class and directed last passage percolation, (3) random matrices, multi-matrix models, and Dyson's Brownian motion. We explain the method and survey results of physical interest.

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“…This observation leads to identifying F k−inst (s) as a k-instanton contribution to the free energy, thereby justifying the notation. 10 Alternatively, one might as well employ asymptotic expansion of the Painlevé II transcendent q(s) for s → ∞ in (3.21) as presented in [48,49]. Concretely, one substitutes a trans-series…”

Section: Jhep09(2014)104mentioning

confidence: 99%

Tracy-Widom distribution as instanton sum of 2D IIA superstrings

Nishigaki

Sugino

2014

J. High Energ. Phys.

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We present an analytic expression of the nonperturbative free energy of a double-well supersymmetric matrix model in its double scaling limit, which corresponds to two-dimensional type IIA superstring theory on a nontrivial Ramond-Ramond background. To this end we draw upon the wisdom of random matrix theory developed by Tracy and Widom, which expresses the largest eigenvalue distribution of unitary ensembles in terms of a Painlevé II transcendent. Regularity of the result at any value of the string coupling constant shows that the third-order phase transition between a supersymmetry-preserving phase and a supersymmetry-broken phase, previously found at the planar level, becomes a smooth crossover in the double scaling limit. Accordingly, the supersymmetry is always broken spontaneously as its order parameter stays nonzero for the whole region of the coupling constant. Coincidence of the result with the unitary one-matrix model suggests that one-dimensional type 0 string theories partially correspond to the type IIA superstring theory. Our formulation naturally allows for introduction of an instanton chemical potential, and reveals the presence of a novel phase transition, possibly interpreted as condensation of instantons.

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Exact Scaling Functions for One-Dimensional Stationary KPZ Growth

Cited by 266 publications

References 34 publications

Slow relaxation and aging kinetics for the driven lattice gas

Slow relaxation and aging kinetics for the driven lattice gas

Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals

Tracy-Widom distribution as instanton sum of 2D IIA superstrings

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