S Shinomoto and Y Kabashima 1991 J. Phys. A: Math. Gen. 24 L141 doi:10.1088/0305-4470/24/3/008
S Shinomoto and Y Kabashima
Show affiliationsThe energy of a local minimum obtained by the simulated annealing generally depends on a time tau in which a complex system has been immersed in a heat bath. How the resultant energy E( tau ) scales with a time tau is an interesting question. The diffusion process of a point in a wiggly parabola is analysed to discuss the scaling. The model is exactly solvable and the energy is found to scale as E( tau )= in +c(ln tau )-1. This scaling is considered rather common to general complex systems. However, the limit in obtained from practical data is not necessarily the ground state energy of a system.
65F35 Matrix norms, conditioning, scaling (See also 15A12, 15A60)
Issue 3 (7 February 1991)
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