Ground-state level spin systems within Bernasconi model

The design problem for law autocorrelation binary sequences (LABS) is a notoriously difficult computational problem which is numbered as the problem number 005 in CSPLib. In statistical physics LABS problem can be interpreted as the energy of N interacting Ising spins. This is a Bernasconi model for a one N-dimensional chain of quantum particles. Ground-state level quantum system within the frame of Bernasconi model is binary sequence with lowest level of peak-sidelobes of aperiodic autocorrelation function. The new results of an exhaustive search for optimal binary sequences with minimum peak sidelobe up to length N=86 are demonstrated. The Bernasconi model exhibits features of a glass transition like a jump in the specific heat and slow dynamics and aging. The Bernasconi model the high temperature phase of Ising spin system reproduces exactly approximation.