### Abstract

We study a model of interface dynamics which describes a surface-tension-biased process of simultaneous deposition and evaporation of particles. The control parameter of the model is the average translational velocity (v) of the interface which is determined by the difference between the rates of deposition and evaporation. For v=0 the dynamics is reversible and the two-dimensional problem can be solved exactly by mapping the system onto a kinetic Ising model. For the case of irreversible growth (v 0), we use Monte Carlo methods to calculate the dynamic structure factor, S(k,t), of the surface. We find that S(k,t) obeys dynamic scaling: S(k,t)k-2+f(kzt) with =0 for all v, whereas z=2 for v=0 and z=(3/2) for v 0. These results suggest that the long-wavelength, long-time limit of our interface model can be described by Burgers equation and, furthermore, that the change in the dynamical exponent z is related to the breaking of time-reversal symmetry which occurs as v becomes nonzero.

Original language | English |
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Pages (from-to) | 3485-3495 |

Number of pages | 11 |

Journal | Physical Review B |

Volume | 35 |

Issue number | 7 |

DOIs | |

Publication status | Published - 1987 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B*,

*35*(7), 3485-3495. https://doi.org/10.1103/PhysRevB.35.3485

**Time-reversal invariance and universality of two-dimensional growth models.** / Plischke, M.; Rácz, Z.; Liu, D.

Research output: Contribution to journal › Article

*Physical Review B*, vol. 35, no. 7, pp. 3485-3495. https://doi.org/10.1103/PhysRevB.35.3485

}

TY - JOUR

T1 - Time-reversal invariance and universality of two-dimensional growth models

AU - Plischke, M.

AU - Rácz, Z.

AU - Liu, D.

PY - 1987

Y1 - 1987

N2 - We study a model of interface dynamics which describes a surface-tension-biased process of simultaneous deposition and evaporation of particles. The control parameter of the model is the average translational velocity (v) of the interface which is determined by the difference between the rates of deposition and evaporation. For v=0 the dynamics is reversible and the two-dimensional problem can be solved exactly by mapping the system onto a kinetic Ising model. For the case of irreversible growth (v 0), we use Monte Carlo methods to calculate the dynamic structure factor, S(k,t), of the surface. We find that S(k,t) obeys dynamic scaling: S(k,t)k-2+f(kzt) with =0 for all v, whereas z=2 for v=0 and z=(3/2) for v 0. These results suggest that the long-wavelength, long-time limit of our interface model can be described by Burgers equation and, furthermore, that the change in the dynamical exponent z is related to the breaking of time-reversal symmetry which occurs as v becomes nonzero.

AB - We study a model of interface dynamics which describes a surface-tension-biased process of simultaneous deposition and evaporation of particles. The control parameter of the model is the average translational velocity (v) of the interface which is determined by the difference between the rates of deposition and evaporation. For v=0 the dynamics is reversible and the two-dimensional problem can be solved exactly by mapping the system onto a kinetic Ising model. For the case of irreversible growth (v 0), we use Monte Carlo methods to calculate the dynamic structure factor, S(k,t), of the surface. We find that S(k,t) obeys dynamic scaling: S(k,t)k-2+f(kzt) with =0 for all v, whereas z=2 for v=0 and z=(3/2) for v 0. These results suggest that the long-wavelength, long-time limit of our interface model can be described by Burgers equation and, furthermore, that the change in the dynamical exponent z is related to the breaking of time-reversal symmetry which occurs as v becomes nonzero.

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U2 - 10.1103/PhysRevB.35.3485

DO - 10.1103/PhysRevB.35.3485

M3 - Article

VL - 35

SP - 3485

EP - 3495

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 7

ER -