Category: Physics

Summary: Testing whether mixed row- and column-correlated disorder produces a less wandering directed-polymer path than either disorder alone.

Directed polymers in random media are a standard model for disorder, localization, and path roughening. This experiment asks what happens when two different anisotropic disorder patterns compete: row-correlated shocks and column-correlated corridor memory. The hypothesis is that combining them can create an intermediate regime where the optimal path wanders less than it does under either pure pattern at matched variance.

The script generates several disorder conditions, solves for the optimal polymer path in each one, and compares path roughness, lateral motion, endpoint spread, and energy density. Rather than a single threshold search, it runs repeated trials and summarizes whether the mixed conditions consistently outperform the pure row-only and column-only cases.

This matters because anisotropic disorder is usually analyzed one mechanism at a time. The experiment probes whether competing anisotropies can jointly suppress wandering and produce a sharper corridor-like localization effect.

Method: Repeated dynamic-programming style optimal-path solves across disorder ensembles, summarized over multiple anisotropic conditions.

What is measured: Mean absolute offset, roughness, lateral motion, endpoint offset, energy density, and mixed-condition gains in wander reduction and energy improvement.