Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
1997-07-16
Phys. Rev. Lett. 78 (1997) 3491-94
Physics
Condensed Matter
Disordered Systems and Neural Networks
4 pages revtex
Scientific paper
10.1103/PhysRevLett.78.3491
A directed polymer is considered on a flat substrate with randomly located parallel ridges. It prefers to lie inside wide regions between the ridges. When the transversel width $W=\exp(\lambda L^{1/3})$ is exponential in the longitudinal length $L$, there can be a large number $\sim \exp L^{1/3}$ of available wide states. This ``complexity'' causes a phase transition from a high temperature phase where the polymer lies in the widest lane, to a glassy low temperature phase where it lies in one of many narrower lanes. Starting from a uniform initial distribution of independent polymers, equilibration up to some exponential time scale induces a sharp dynamical transition. When the temperature is slowly increased with time, this occurs at a tunable temperature. There is an asymmetry between cooling and heating. The structure of phase space in the low temperature non-equilibrium glassy phase is of a one-level tree.
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