Replica Field Theory for Deterministic Models: Binary Sequences with Low Autocorrelation

Details Replica Field Theory for Deterministic Models: Binary Sequences with Low Autocorrelation Replica Field Theory for Deterministic Models: Binary Sequences with Low Autocorrelation

1994-05-23

arxiv.org/abs/hep-th/9405148v1

J.Phys. A27 (1994) 7615-7646

Physics

High Energy Physics

High Energy Physics - Theory

42 pages, uufile with eps figures added in figures, ROM2F/94/15

Scientific paper

10.1088/0305-4470/27/23/010

We study systems without quenched disorder with a complex landscape, and we use replica symmetry theory to describe them. We discuss the Golay-Bernasconi-Derrida approximation of the low autocorrelation model, and we reconstruct it by using replica calculations. Then we consider the full model, its low $T$ properties (with the help of number theory) and a Hartree-Fock resummation of the high-temperature series. We show that replica theory allows to solve the model in the high $T$ phase. Our solution is based on one-link integral techniques, and is based on substituting a Fourier transform with a generic unitary transformation. We discuss this approach as a powerful tool to describe systems with a complex landscape in the absence of quenched disorder.

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