1993/09/14 by Terence Hwa, Daniel S. Fisher · 6 citations
Materials Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Condensed matter physics #Degenerate energy levels #Distribution (mathematics) #Material Dynamics and Properties #Mathematical analysis #Mathematics #Physics #Power law #Quantum mechanics #Replica #Scaling #Statistical physics #Symmetry (geometry) #Symmetry breaking #Theoretical and Computational Physics #Thermal fluctuations #Tilt (camera) #cond-mat
paper · pdf · doi:10.1103/physrevb.49.3136
59 pages including 8 figures ( REVTEX 3.0 )E-mail: [email protected]
arxiv created 1993/09/14 · openalex publication_date 1994/02/01 · arxiv updated 2016/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A systematic analysis of large-scale fluctuations in the low-temperature pinned phase of a directed polymer in a random potential is described. These fluctuations come from rare regions with nearly degenerate ``ground states.'' The probability distribution of their sizes is found to have a power-law tail. The rare regions in the tail dominate much of the physics. The analysis presented here takes advantage of the mapping to the noisy Burgers' equation. It complements a phenomenological description of glassy phases based on a scaling picture of droplet excitations and a recent variational approach with ``broken replica symmetry.'' It is argued that the power-law distribution of large thermally active excitations is a consequence of the continuous statistical ``tilt'' symmetry of the directed polymer, the breaking of which gives rise to the large active excitations in a manner analogous to the appearance of Goldstone modes in pure systems with a broken continuous symmetry.