Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
1997-01-02
Physical Review E 55, 3934 (1997)
Physics
Condensed Matter
Disordered Systems and Neural Networks
8 pages, LaTex, PostScript-figures included but also available upon request. To be published in Physical Review E (01/March 97
Scientific paper
10.1103/PhysRevE.55.3934
The multifractal properties of the Edwards-Anderson order parameter of the short-range Ising spin glass model on d=3 diamond hierarchical lattices is studied via an exact recursion procedure. The profiles of the local order parameter are calculated and analysed within a range of temperatures close to the critical point with four symmetric distributions of the coupling constants (Gaussian, Bimodal, Uniform and Exponential). Unlike the pure case, the multifractal analysis of these profiles reveals that a large spectrum of the $\alpha $-H\"older exponent is required to describe the singularities of the measure defined by the normalized local order parameter, at and below the critical point. Minor changes in these spectra are observed for distinct initial distributions of coupling constants, suggesting an universal spectra behavior. For temperatures slightly above T_{c}, a dramatic change in the $F(\alpha)$ function is found, signalizing the transition.
Edvaldo Nogueira Jr.
Coutinho Sérgio
Curado Evaldo M. F.
de Almeida R. L. J.
Nobre Fernando D.
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