On the ground states of the Bernasconi model

Abstract

The ground states of the Bernasconi model are binary +1/-1 sequences of length N with low autocorrelations. We introduce the notion of perfect sequences, binary sequences with one-valued off-peak correlations of minimum amount. If they exist, they are ground states. Using results from the mathematical theory of cyclic difference sets, we specify all values of N for which perfect sequences do exist and how to construct them. For other values of N, we investigate almost perfect sequences, i.e. sequences with two-valued off-peak correlations of minimum amount. Numerical and analytical results support the conjecture that almost perfect sequences do exist for all values of N, but that they are not always ground states. We present a construction for low-energy configurations that works if N is the product of two odd primes.

12 pages, LaTeX2e; extended content, added references; submitted to J.Phys.A

References in corpus (6)

• Replica Field Theory for Deterministic Models (II): A Non-Random Spin Glass with Glassy Behavior
• Replica Field Theory for Deterministic Models: Binary Sequences with Low Autocorrelation
• Self Induced Quenched Disorder: A Model for the Glass Transition
• Exhaustive search for low autocorrelation binary sequences
• Aging without disorder on long time scales
• Ground states for a class of deterministic spin models with glassy behaviour

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