Samples: 0
Mean F: 0.00
Std dev σ: 0.00
Skewness: 0.00
χ (KPZ): ~0.33
Directed polymer in random media (DPRM): a 1D polymer of length N is directed along the time axis, with each step moving ±1 in space through a random energy landscape η(x,t). The partition function Z = Σ exp(−βE[path]) over all directed paths.
The free energy F = −(1/β) ln Z fluctuates across disorder realizations. The KPZ universality class predicts: Var(F) ~ N^(2β_KPZ) with β_KPZ = 1/3, and the fluctuation distribution converges to the Tracy-Widom GUE distribution — the same law governing the largest eigenvalue of random Hermitian matrices.
The histogram shows sampled free energies. The slight negative skewness (~−0.29) is characteristic of Tracy-Widom. The optimal path (shown in gold) minimizes energy through the disorder landscape.