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The ground state of interacting particles on a disordered one-dimensionalhost-lattice is studied by a direct numerical method. It is shown that if theconcentration of particles is small, then even a weak disorder of thehost-lattice breaks the long-range order of Generalized Wigner Crystal,replacing it by the sequence of blocks (domains) of particles with randomlengths. The mean domains length as a function of the host-lattice disorderparameter is also found. It is shown that the domain structure can be detectedby a weak random field, whose form is similar to that of the ground state buthas fluctuating domain walls positions. This is because the generalizedmagnetization corresponding to the field has a sufficiently sharp peak as afunction of the amplitude of fluctuations for small amplitudes.

The ground state structure of electron's ensemble on one-dimension disordered lattice