Category: Physics

Summary: Comparing how quickly different disorder distributions approach the KPZ fluctuation exponent in a directed-polymer model.

Directed polymers in random media are a central route into KPZ universality, where free-energy fluctuations are expected to scale with exponent one third. This experiment asks not just whether that exponent appears, but how the rate of convergence depends on the underlying disorder distribution.

The script simulates a one-plus-one-dimensional directed polymer, computes the partition function and free-energy statistics across timescales, and compares exponential, uniform, and lognormal disorder. It also checks skewness against Tracy-Widom expectations to see how distributional shape approaches the universal prediction.

That comparative approach is useful because universality does not imply equal finite-size behavior. The experiment focuses on the structure of convergence, not only the asymptotic claim.

Method: Repeated lattice directed-polymer simulations with free-energy fluctuation analysis across multiple disorder families.

What is measured: Effective KPZ fluctuation exponent, variance scaling, free-energy skewness, disorder-distribution dependence, and convergence rate.