Complete Scaling Theory Research Articles

Percolation Quantum Phase Transitions in Diluted Magnets

We show that the interplay of geometric criticality and quantum fluctuations leads to a novel universality class for the percolation quantum phase transition in diluted magnets. All critical exponents involving dynamical correlations are different from the classical percolation values, but in two dimensions they can nonetheless be determined exactly. We develop a complete scaling theory of this transition, and we relate it to recent experiments in La2Cu(1-p)(Zn,Mg)(p)O4. Our results are also relevant for disordered interacting boson systems.

Gauge invariance and the multiplicative renormalisation group in the Anderson transition

The linear response to an electromagnetic field of a gas of particles in a random on-site potential is studied within the ordinary many-body theory and the multiplicative renormalisation group. The crucial role played by the gauge invariance in determining the renormalisation procedure and thus the critical indices is emphasised by means of the use of the corresponding Ward identities. In this way it is possible to rederive a complete scaling theory of the localisation transition. A gauge-invariant expansion in terms of the inverse conductance around the lower critical dimensionality two leads then to the epsilon -expansion for the critical indices, which was previously derived by referring to an analogy with the non-linear sigma model.