Like critical phenomena, hydrodynamics, and reaction-diffusion systems,
also heat conduction shows anomalous behaviour in low enough dimensions.
More precisely, the conductivity in generic 2-d models diverges logarithmically
with system size, while it diverges as a power of the system size in d=1.
We verified this behaviour numerically for a 1-d hard particle gas where
previous simulations had given conflicting results, and conjectured that
the main exponent is explained by Kardar-Parisi-Zhang theory which essentially
describes the hydrodynamics of the energy flow. For elongated rectangular
2-d lattices with periodic lateral boundary conditions (i.e., for cylinders)
we studied in detail the cross-over from the 1-d to the 2-d behaviour,
and predicted from this a heat conduction anomaly in carbon nanotubes.
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