(1) Institute of Molecular Physics, Polish Academy of Sciences, Smoluchowskiego 17/19, 60-179 Poznań, Poland, PL
Abstract:
Scaling properties of the Gibbs distribution of a finite-size one-dimensional Ising model are investigated as the thermodynamic
limit is approached. It is shown that, for each nonzero temperature, coarse-grained probabilities of the appearance of particular
energy levels display multiscaling with the scaling length ℓ = 1/Mn, where n denotes the number of spins and Mn is the total number of energy levels. Using the multifractal formalism, the probabilities are argued to reveal also multifractal
properties.
Received 10 July 2000 and Received in final form 6 November 2000