Different facets of the raise and peel model

Alcaraz, Francisco C.; Rittenberg, V.

doi:10.1088/1742-5468/2007/07/p07009

Cited by 15 publications

(70 citation statements)

References 53 publications

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“…One clearly sees data collapse already for relatively small lattice sizes, and no discontinuity is observed. Moreover the value 0.31, at the density at η = 0 is compatible with the known result [16] for the open system. This observation made us think that may be the phase transition is a red herring.…”

supporting

confidence: 90%

“…We consider this case first. We should expect on dimensional grounds and conformal invariance that, in the large L limit, the current to be of the form (1.1), with the sound velocity v s = 3 √ 3/2 [16] and C an universal constant. Based on numerical data on lattices up to 18, Pyatov [23] made the following conjecture for the current (L even)…”

Section: Representations Of the Temperley-lieb And Periodicmentioning

confidence: 99%

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Nonlocal asymmetric exclusion process on a ring and conformal invariance

Alcaraz¹,

Rittenberg²

2013

J. Stat. Mech.

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We present a one-dimensional nonlocal hopping model with exclusion on a ring. The model is related to the Raise and Peel growth model. A nonnegative parameter u controls the ratio of the local backwards and nonlocal forwards hopping rates. The phase diagram and consequently the values of the current, depend on u and the density of particles. In the special case of half-filling and u = 1 the system is conformal invariant and an exact value of the current for any size L of the system is conjectured and checked for large lattice sizes in Monte Carlo simulations. For u > 1 the current has a non-analytic dependence on the density when the latter approaches the half-filling value.

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supporting

confidence: 90%

Section: Representations Of the Temperley-lieb And Periodicmentioning

confidence: 99%

Nonlocal asymmetric exclusion process on a ring and conformal invariance

Alcaraz¹,

Rittenberg²

2013

J. Stat. Mech.

Self Cite

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“…The density of contact points estimator was computed using an almost rigorously derived expression [23] for the density of contact points:…”

Section: Shared Information In the Raise And Peel Modelmentioning

confidence: 99%

Shared information in stationary states at criticality

Alcaraz¹,

Rittenberg²

2010

J. Stat. Mech.

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We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the shared information between the two subsystems. If the correlation length is finite, the estimators stay finite for large system sizes. If the correlation length diverges, so do the estimators. The definition of the estimators is inspired by information theory. We look at several models and compare the behavior of the estimators in the finite-size scaling limit. Analytical and numerical methods as well as Monte Carlo simulations are used. We show how the finite-size scaling functions change for various phase transitions, including the case where one has conformal invariance.

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“…Excluded are (i) systems that exhibit long-range order in the stationary state, in which case complex characteristic velocities indicative of phase separation [34,35] may arise. (ii) In systems with long-range interactions other discrete dynamical exponents may appear, e.g., the ballistic universality class with z = 1 in nearest-neighbour hopping with long-range dependence of the hopping rate [36,37,38], or in models with long-range jumps such as the Oslo rice pile model with z = 10/7 [39] or the raise-and-peel model [40], also with z = 1. (iii) Also integrable models with non-local conservation laws might conceivably exhibit dynamical exponents that are not Kepler ratios.…”

Section: Nonlinear Fluctuating Hydrodynamicsmentioning

confidence: 99%

Kardar-Parisi-Zhang modes in d -dimensional directed polymers

Schütz

Wehefritz-Kaufmann

2017

Phys. Rev. E

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We define a stochastic lattice model for a fluctuating directed polymer in d 2 dimensions. This model can be alternatively interpreted as a fluctuating random path in two dimensions, or a one-dimensional asymmetric simple exclusion process with d − 1 conserved species of particles. The deterministic large dynamics of the directed polymer are shown to be given by a system of coupled Kardar-Parisi-Zhang (KPZ) equations and diffusion equations. Using nonlinear fluctuating hydrodynamics and mode coupling theory we argue that stationary fluctuations in any dimension d can only be of KPZ type or diffusive. The modes are pure in the sense that there are only subleading couplings to other modes, thus excluding the occurrence of modified KPZ-fluctuations or Lévy-type fluctuations, which are common for more than one conservation law. The mode-coupling matrices are shown to satisfy the so-called trilinear condition.

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Different facets of the raise and peel model

Cited by 15 publications

References 53 publications

Nonlocal asymmetric exclusion process on a ring and conformal invariance

Nonlocal asymmetric exclusion process on a ring and conformal invariance

Shared information in stationary states at criticality

Kardar-Parisi-Zhang modes in d -dimensional directed polymers

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