Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-01-26
Physics
Condensed Matter
Statistical Mechanics
16 pages, 2 figures, submitted to Phys. Rev. E, references added, few typos corrected
Scientific paper
10.1103/PhysRevE.64.051910
We study the Langevin dynamics of the standard random heteropolymer model by mapping the problem to a supersymmetric field theory using the Martin-Siggia-Rose formalism. The resulting model is solved non-perturbatively employing a Gaussian variational approach. In constructing the solution, we assume that the chain is very long and impose the translational invariance which is expected to be present in the bulk of the globule by averaging over the center the of mass coordinate. In this way we derive equations of motion for the correlation and response functions C(t,t') and R(t,t'). The order parameters are extracted from the asymptotic behavior of these functions. We find a dynamical phase diagram with frozen (glassy) and melted (ergodic) phases. In the glassy phase the system fails to reach equilibrium and exhibits aging of the type found in p-spin glasses. Within the approximations used in this study, the random heteropolymer model can be mapped to the problem of a manifold in a random potential with power law correlations.
Franz Silvio
Hertz John
Konkoli Zoran
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