Replica field theory for deterministic models: I. Binary sequences with low autocorrelation

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. We then 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 us 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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