Low-temperature thermodynamics of one-dimensional Wigner glass on a highly disordered host lattice

The low-temperature thermodynamics of one-dimensional (1D) Wigner glass on a disordered lattice (WGDOHL), which comes to existence when the inter-electron distances exceed noticeably the inter-site ones, has been studied. An efficient computer procedure, based on the presentation of the statistical sum as a product of random transfer-matrixes, has been developed for calculations of thermodynamic characteristics of the system under consideration. The lattice structures were varied from completely chaotic up to strictly regular ones. It has been established that for any degree of disorder the entropy and heat capacity of the system tend to zero linearly as the temperature is reduced. It is shown that the spectrum of elementary excitations has gapless structure. An instability of 1D WGODHL has been revealed: under conditions of vanishingly small disordering of the lattice, the long-range order in 1D WGODHL is broken by frustrations that are 1D analogs of the frustrations in two- and three-dimensional spin glasses.