Directed Paths in Random Media

Details Directed Paths in Random Media Directed Paths in Random Media

1994-10-31

arxiv.org/abs/cond-mat/9411022v1

Physics

Condensed Matter

75 pages. Lectures presented at 1994 Les Houches Summer School ``Fluctuating Geometries in Statistical Mechanics and Field The

Scientific paper

Contents: A. Introduction B. High Temperature Expansions for the Ising Model C. Characteristic Functions and Cumulants D. The One Dimensional Chain E. Directed Paths and the Transfer Matrix F. Moments of the Correlation Function G. The Probability Distribution in Two Dimensions H. Higher Dimensions I. Random Signs J. Other Realizations of DPRM K. Quantum Interference of Strongly Localized Electrons L. The Locator Expansion and Forward Scattering Paths M. Magnetic Field Response N. Unitary Propagation O. Unitary Averages P. Summing all Paths in High Dimensions Q. The Ising Model on a Square Lattice R. Singular Behavior S. The Two Dimensional Spin Glass T. Results for the Two Dimensional Spin Glass

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