Related Experiment Video
Updated: Aug 13, 2025

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
Published on: March 1, 2022
Kardar-Parisi-Zhang universality class in (d+1)-dimensions
1Departamento de Física, Universidade Federal de Viçosa, 36570-900 Viçosa, MG, Brazil.
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 β_{d}=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.
Related Concept Videos
Second Uniqueness Theorem
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the...
Collisions in Multiple Dimensions: Introduction
The Pauli Exclusion Principle
Dimensionless Groups in Fluid Mechanics
Space-Time Curvature and the General Theory of Relativity
This has been verified in many experiments. However, space and time are no longer absolute. Two observers moving relative to one another do not agree on the length of objects or the passage of time. The mechanics of objects based on Newton's laws of...
Routh-Hurwitz Criterion I
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...

