By Dietrich Stauffer (auth.), H. Eugene Stanley, Nicole Ostrowsky (eds.)

ISBN-10: 079231011X

ISBN-13: 9780792310112

ISBN-10: 9400921578

ISBN-13: 9789400921573

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Extra info for Correlations and Connectivity: Geometric Aspects of Physics, Chemistry and Biology

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R __ ' - 0" _ •••••••••• _ . ... . . . . . . . . . . . . . . . . , _ b) ur Fig. ) at Te if = -1 is fixed in a L=60 system (a) and (b) and if the damage is fixed on the boundary of a L = 100 system (c) for the 2d Ising model with heat bath dynamics. Figure (b) shows the evolution of cluster (a) after 38 time steps (from Ref. 7). 8) where the damage after a time t is different than zero and independent of the initial damage D(O); (III) A low temperature phase (T < T2 ) where the damage is different than zero but depends on the initial damage.

In §3 some exact results are presented on the fractal structure of these clusters at criticality, based on a mapping between the Potts model and the Coulomb gas. In §4 the extension of these geometrical concepts to the Ising spin glasses will be presented. 2. The Correct Clusters Consider a ferromagnetic Ising model with zero external field. The Hamiltonian for nearest neighbor (nn) interactions can be written as: -1i == J 2: S;Sj, <;j> * Lecture notes prepared by Jysoo Lee and Son a Prakash. 21 H.

Phys. Lett. (Paris) 46, L149 (1985). 26. H. Saleur and B. Duplantier, Phys. Rev. Lett. 58, 2325 (1987). 27. L. de Arcangelis, unpublished. 28. B. B. Mandelbrot and J. Given, Phys. Rev. Lett 52, 1853 (1984); see also B. B. Mandelbrot, J. Stat. Phys. 34, 895 (1984). 29. M. Mezard, G. Parisi and M. A. Virasoro, Spin Gla .. Theory and Beyond (World Scientific, Singapore, 1987). 30. A. Coniglio, F. di Liberto, G. Monroy and F. Peruggi, to be published. 31. G. Parisi private communication. 32. L. de Arcangelis and A.

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Correlations and Connectivity: Geometric Aspects of Physics, Chemistry and Biology by Dietrich Stauffer (auth.), H. Eugene Stanley, Nicole Ostrowsky (eds.)


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