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• W2040571911 endingPage "115002" @default.
• W2040571911 startingPage "115002" @default.
• W2040571911 abstract "We consider various random models (directed polymer, random ferromagnets, spin-glasses) in their disorder-dominated phases, where the free-energy cost $F(L)$ of an excitation of length $L$ presents fluctuations that grow as a power-law $Delta F(L) sim L^{theta}$ with the 'droplet' exponent $theta$. Within the droplet theory, the energy and entropy of such excitations present fluctuations that grow as $Delta E(L) sim Delta S(L) sim L^{d_s/2}$ where $d_s$ is the dimension of the surface of the excitation. These systems usually present a positive 'chaos' exponent $zeta=d_s/2-theta>0$, meaning that the free-energy fluctuation of order $L^{theta}$ is a near-cancellation of much bigger energy and entropy fluctuations of order $L^{d_s/2}$. Within the standard droplet theory, the dynamics is characterized by a barrier exponent $psi$ satisfying the bounds $theta leq psi leq d-1$. In this paper, we argue that a natural value for this barrier exponent is $psi=d_s/2$ : (i) for the directed polymer where $d_s=1$, this corresponds to $psi=1/2$ in all dimensions; (ii) for disordered ferromagnets where $d_s=d-1$, this corresponds to $psi=(d-1)/2$; (iii) for spin-glasses where interfaces have a non-trivial dimension $d_s$ known numerically, our conjecture $psi=d_s/2$ gives numerical predictions in $d=2$ and $d=3$. We compare these values with the available numerical results for each case, in particular with the measure $psi simeq 0.49$ of Kolton, Rosso, Giamarchi, Phys. Rev. Lett. 95, 180604 (2005) for the non-equilibrium dynamics of a directed elastic string." @default.
• W2040571911 created "2016-06-24" @default.
• W2040571911 creator A5060853119 @default.
• W2040571911 creator A5090565816 @default.
• W2040571911 date "2008-03-04" @default.
• W2040571911 modified "2023-10-16" @default.
• W2040571911 title "Non-equilibrium dynamics of polymers and interfaces in random media: conjecture ψ =ds/2 for the barrier exponent" @default.
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• W2040571911 doi "https://doi.org/10.1088/1751-8113/41/11/115002" @default.
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