https://doi.org/10.1007/s100510170358
Multiscaling and multifractality in an one-dimensional Ising model
Institute of Molecular Physics, Polish Academy of Sciences,
Smoluchowskiego 17/19, 60-179 Poznań, Poland
Corresponding author: a jezewski@ifmpan.poznan.pl
Received:
10
July
2000
Revised:
6
November
2000
Published online: 15 January 2001
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 
, 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.
PACS: 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 05.70.-a – Thermodynamics / 64.10.+h – General theory of equations of state and phase equilibria / 68.35.Rh – Phase transitions and critical phenomena
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001
