Kardar-Parisi-Zhang universality class in ($d+1$)-dimensions

Abstract

The determination of the exact exponents of the KPZ class in any substrate dimension $d$ is one of the most important open issues in Statistical Physics. Based on the behavior of the dimensional variation of some exact exponent differences for other growth equations, I find here that the KPZ growth exponents (related to the temporal scaling of the fluctuations) are given by ${\beta }_d=\frac{7}{8d+13}$. These exponents present an excellent agreement with the most accurate estimates for them in the literature. Moreover, they are confirmed here through extensive Monte Carlo simulations of discrete growth models and real space renormalization group (RG) calculations for directed polymers in random media (DPRM), up to $d=15$. The left-tail exponents of the probability density functions for the DPRM energy provide another striking verification of the analytical result above.

6 pages, 3 figures, 2 tables

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Cited by in corpus (7)

• Universal scaling relation for growth phenomena
• Kardar-Parisi-Zhang scaling in time-crystalline matter
• Phase diagram and universal scaling regimes of two-dimensional exciton-polariton Bose-Einstein condensates
• One-point height fluctuations and two-point correlators of $(2+1)$ cylindrical KPZ systems
• Numerical Integration of the KPZ and Related Equations on Networks: The Case of the Cayley Tree
• Dimensional crossover in Kardar-Parisi-Zhang growth
• Dimensional crossover in surface growth on rectangular substrates