Statistical mechanics of the travelling salesman on the Sierpinski gasket

R.M. Bradley

We study the statistical mechanics of the travelling salesman on a Sierpinski gasket in which the bond lengths { λi } are quenched random variables. The problem of finding the shortest closed path which visits all N sites is tractable if all the| λi — 1 | are less than (2 N + 1)-1. For a particular choice of the bond-length probability distribution and at low temperatures, the system behaves like a set of non-interacting Ising spins in a quenched random magnetic field. The relevance of one of our results to collapsed polymer chains in random media is also discussed.

Mots clés: operations research; statistical mechanics

Domaines: Articles anciens

R.M. Bradley. Statistical mechanics of the travelling salesman on the Sierpinski gasket. Journal de Physique, 1986, 47 (1), pp.9-14. ⟨10.1051/jphys:019860047010900⟩. ⟨jpa-00210189⟩