Dynamic phase diagram of the Number Partitioning Problem

Details Dynamic phase diagram of the Number Partitioning Problem Dynamic phase diagram of the Number Partitioning Problem

2004-08-23

arxiv.org/abs/cond-mat/0408484v1

Phys. Rev. E 70, 066126 (2004)

Physics

Condensed Matter

Disordered Systems and Neural Networks

15 pages, submitted to PRE

Scientific paper

10.1103/PhysRevE.70.066126

We study the dynamic phase diagram of a spin model associated with the Number Partitioning Problem, as a function of temperature and of the fraction $K/N$ of spins allowed to flip simultaneously. The case K=1 reproduces the activated behavior of Bouchaud's trap model, whereas the opposite limit $K=N$ can be mapped onto the entropic trap model proposed by Barrat and M\'ezard. In the intermediate case $1 \ll K \ll N$, the dynamics corresponds to a modified version of the Barrat and M\'ezard model, which includes a slow (rather than instantaneous) decorrelation at each step. A transition from an activated regime to an entropic one is observed at temperature $T_g/2$ in agreement with recent work on this model. Ergodicity breaking occurs for $T

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