Zero-temperature phase transitions in quantum systems with symmetry-conserving impurities

Abstract

Abstract The zero-temperature phase transitions in several quantum systems with quenched symmetry-conserving impurities are investigated on the grounds of a diagrammatic approach, starting from an appropriate random quantum field functional Hamiltonian. We find that the peculiar random anisotropy induced along the imaginary-time axis by the competition between random and quantum regime fluctuations inhibits the occurence of a sharp second-order transition, in agreement with the renormalization group predictions. In particular, for three-dimensional Ising-like systems a spin-glass-like behavior appears, while for systems with continuous symmetry only smeared or first-order transitions seem to be possible. An explicit calculation in the large- n limit suggests that the second alternative is more realistic. Additional insight is obtained by reformulating the problem by means of Bogolubov's variational principle. Its intrinsic simplicity gives the possibility to obtain informations for dimensionalities d > 1 and offers the occasion for some methodological remarks. Finally, in the light of our results, we put forward a possible interpretation of recent experiments on some mixed crystals.