Universality classes of the Kardar-Parisi-Zhang equation. (English) Zbl 1228.82068
Summary: We reexamine mode-coupling theory for the Kardar-Parisi-Zhang equation in the strong-coupling limit and show that there exist two branches of solutions. One branch (or universality class) exists only for dimensionalities \(d<d_c=2\) and is similar to that found by a variety of analytic approaches, including replica symmetry breaking and Flory-Imry-Ma arguments. The second branch exists up to \(d_c=4\) and gives values for the dynamical exponent \(z\) similar to those of numerical studies for \(d\geq2\).
MSC:
82C27 | Dynamic critical phenomena in statistical mechanics |
82C24 | Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics |
82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
References:
[1] | DOI: 10.1103/PhysRevLett.56.889 · Zbl 1101.82329 · doi:10.1103/PhysRevLett.56.889 |
[2] | DOI: 10.1016/0370-1573(94)00087-J · doi:10.1016/0370-1573(94)00087-J |
[3] | DOI: 10.1080/00018739700101498 · doi:10.1080/00018739700101498 |
[4] | DOI: 10.1103/PhysRevA.16.732 · doi:10.1103/PhysRevA.16.732 |
[5] | DOI: 10.1016/0550-3213(87)90203-3 · doi:10.1016/0550-3213(87)90203-3 |
[6] | DOI: 10.1103/PhysRevLett.54.2026 · doi:10.1103/PhysRevLett.54.2026 |
[7] | DOI: 10.1007/BF01726201 · doi:10.1007/BF01726201 |
[8] | DOI: 10.1103/PhysRevLett.69.1552 · doi:10.1103/PhysRevLett.69.1552 |
[9] | DOI: 10.1103/PhysRevA.44.R7873 · doi:10.1103/PhysRevA.44.R7873 |
[10] | DOI: 10.1103/PhysRevLett.74.4257 · doi:10.1103/PhysRevLett.74.4257 |
[11] | DOI: 10.1103/PhysRevE.47.R1455 · doi:10.1103/PhysRevE.47.R1455 |
[12] | DOI: 10.1103/PhysRevLett.62.442 · doi:10.1103/PhysRevLett.62.442 |
[13] | DOI: 10.1103/PhysRevLett.94.195702 · doi:10.1103/PhysRevLett.94.195702 |
[14] | DOI: 10.1103/PhysRevLett.86.3946 · doi:10.1103/PhysRevLett.86.3946 |
[15] | DOI: 10.1103/PhysRevE.63.057103 · doi:10.1103/PhysRevE.63.057103 |
[16] | DOI: 10.1103/PhysRevE.65.017105 · doi:10.1103/PhysRevE.65.017105 |
[17] | DOI: 10.1103/PhysRevB.68.174202 · doi:10.1103/PhysRevB.68.174202 |
[18] | DOI: 10.1103/PhysRevE.72.035101 · doi:10.1103/PhysRevE.72.035101 |
[19] | DOI: 10.1051/jp1:1991171 · doi:10.1051/jp1:1991171 |
[20] | DOI: 10.1103/PhysRevB.55.226 · doi:10.1103/PhysRevB.55.226 |
[21] | DOI: 10.1103/PhysRevE.69.061112 · doi:10.1103/PhysRevE.69.061112 |
[22] | DOI: 10.1103/PhysRevA.45.7162 · doi:10.1103/PhysRevA.45.7162 |
[23] | DOI: 10.1007/BF01048047 · Zbl 1097.82544 · doi:10.1007/BF01048047 |
[24] | DOI: 10.1103/PhysRevE.65.026136 · doi:10.1103/PhysRevE.65.026136 |
[25] | DOI: 10.1088/0305-4470/33/46/303 · Zbl 0970.82023 · doi:10.1088/0305-4470/33/46/303 |
[26] | DOI: 10.1103/PhysRevLett.80.3527 · doi:10.1103/PhysRevLett.80.3527 |
[27] | DOI: 10.1103/PhysRevE.59.6460 · doi:10.1103/PhysRevE.59.6460 |
[28] | DOI: 10.1103/PhysRevLett.72.2041 · Zbl 0935.82028 · doi:10.1103/PhysRevLett.72.2041 |
[29] | DOI: 10.1103/PhysRevE.53.4424 · doi:10.1103/PhysRevE.53.4424 |
[30] | DOI: 10.1023/B:JOSS.0000019810.21828.fc · Zbl 1157.82363 · doi:10.1023/B:JOSS.0000019810.21828.fc |
[31] | DOI: 10.1023/B:JOSS.0000026730.76868.c4 · Zbl 0963.82033 · doi:10.1023/B:JOSS.0000026730.76868.c4 |
[32] | DOI: 10.1209/epl/i1999-00343-4 · doi:10.1209/epl/i1999-00343-4 |
[33] | DOI: 10.1088/0305-4470/11/7/023 · doi:10.1088/0305-4470/11/7/023 |
[34] | DOI: 10.1088/0305-4470/21/22/019 · doi:10.1088/0305-4470/21/22/019 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.