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Article Dans Une Revue Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Année : 2006

Statistics of low energy excitations for the directed polymer in a 1+d random medium (d = 1, 2, 3)

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We consider a directed polymer of length L in a random medium of space dimension d=1,2,3. The statistics of low energy excitations as a function of their size l is numerically evaluated. These excitations can be divided into bulk and boundary excitations, with respective densities ρbulkL(E=0,l) and ρboundaryL(E=0,l). We find that both densities follow the scaling behavior ρbulk,boundaryL(E=0,l)=L−1−θdRbulk,boundary(x=l∕L), where θd is the exponent governing the energy fluctuations at zero temperature (with the well-known exact value θ1=1∕3 in one dimension). In the limit x=l∕L→0, both scaling functions Rbulk(x) and Rboundary(x) behave as Rbulk,boundary(x)∼x−1−θd, leading to the droplet power law ρbulk,boundaryL(E=0,l)∼l−1−θd in the regime 1⪡l⪡L. Beyond their common singularity near x→0, the two scaling functions Rbulk,boundary(x) are very different: whereas Rbulk(x) decays monotonically for 0
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hal-00172803 , version 1 (21-04-2023)

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Cecile Monthus, Thomas Garel. Statistics of low energy excitations for the directed polymer in a 1+d random medium (d = 1, 2, 3). Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2006, 73 (5), pp.056106. ⟨10.1103/PhysRevE.73.056106⟩. ⟨hal-00172803⟩
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