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Review on relationship between the universality class of the Kardar-Parisi-Zhang equation and the ballistic deposition model

Sayfidinov Okhunjon, Bognar Gabriella

International Journal of Applied Mechanics and Engineering

2021

Vol. 26, no. 4

206--216

We have analysed the research findings on the universality class and discussed the connection between the Kardar-Parisi-Zhang (KPZ) universality class and the ballistic deposition model in microscopic rules. In one dimension and 1+1 dimensions deviations are not important in the presence of noise. At the same time, they are very relevant for higher dimensions or deterministic evolution. Mostly, in the analyses a correction scale higher than 1280 has not been studied yet. Therefore, the growth of the interface for finite system size [...] value predicted by the KPZ universality class is still predominant. Also, values of [...] obtained from literature are consistent with the expected KPZ values of [...] connection between the ballistic deposition and the KPZ equation through the limiting procedure and by applying the perturbation method was also presented.

Finite-size analysis via the critical energy-subspace method in the Ising models

Malakis A. C., Hadjiagapiou I. A., Martinos S. S., Fytas N. G.

Materials Science Poland

2005

Vol. 23, No. 4

947--954

We briefly review some applications of the critical minimum energy-subspace method (CrMES) using the Wang?Landau sampling for the estimation of the density of states (DOS). These applications concern the two- and three-dimensional Ising models and their important conserved order parameter versions (COP), known also as the Ising models with fixed magnetization (IMFM). The recently developed CrMES scheme greatly facilitates methods for sampling the DOS of classical statistical models in large systems. In effect, the CrMES technique enables the estimation of critical behaviour using only a small part of the energy space. Specific heat curves are obtained, their peaks are located and their scaling behaviour is studied and compared with the results known from literature whenever such results exist.