Quantum XY and Heisenberg models on the planar lattices — the renormalization group approach

Abstract

Within a real-space renormalization group framework, the critical behaviour of the spin 1 2 quantum XY and Heisenberg models on the three planar lattices has been studied. We have restricted ourselves to ferromagnetic-like case. It has been shown that there is a nontrivial fixed point and corresponding critical temperature for the nearest-neighbour XY model for each 2d lattice. Concerning the Heisenberg model, to first order in cumulant expansion there is no nontrivial fixed point, however, it appears in the second and third order calculations. This suggests that 2d Heisenberg model also exhibits some kind of a critical behaviour.