Critical behaviour of a one-dimensional crystal at the displacive limit

Arno Holz, J.T.N. Medeiros

Quantum effects on the static critical behaviour of an isotropic n-vector model undergoing a displacement-type phase transition are studied at T c and to O(1/n). For T c not=0 there is no quantum effect on eta , and for T c =0 one gets eta =0 for d>3, and for 2<d<3 eta is due to quantum fluctuations, implying that it assumes a different value than in the classical case. The dynamical behaviour of the system violates the dynamic scaling hypothesis.

V. N. Bogomolov, E.V. Kolla, Yu. A. Kumzerov

Marc Siegmund, Markus Hofmann, Oleg Pankratov

We use Density Functional Theory to study interacting spinless electrons on a one-dimensional quantum ring in the density range where the system undergoes Wigner crystallization. The Wigner transition leads to a drastic ``collective'' electron localization due to the Wigner crystal pinning, provided a weak impurity potential is applied. To reveal this localization we examine a persistent current in a ring penetrated by a magnetic flux. Using the DFT-OEP method we calculated the current as a function of the interaction parameter r_S. We find that in the limit of vanishing impurity potential the persistent current stays constant up to a critical value of r_S^c=2.05 but shows a drastic exponential decay for larger r_S which reflects a formation of a pinned Wigner crystal. Above r_S^c the amplitude of the electron density oscillations exactly follows the (r_S-r_S^c)^{1/2} behaviour, confirming a second-order phase transition as expected in the mean-field-type OEP approximation.

V. Rizi, S. K. Ghosh

博 池田

Paul R. Gerber

A classical n-vector model is considered which is infinitely extended in d-1 dimensions and periodic of period b in the dth dimension. Asymptotically for large values of b the critical temperature is expected to obey a scaling law T c (b)-T c ( infinity ) approximately Ab - lambda . The authors have calculated the shift exponent lambda to first order in a 1/n expansion for dimensions between three and four. To this order the result is consistent with the assertion lambda = nu d -1 where nu d is the correlation length exponent of the infinitely extended d-dimensional system. From the equivalence between this model and (d-1)-dimensional quantum mechanical systems the behaviour of critical lines near the displacive limit (T c =0) can be derived.