Bose expansion and investigation of the critical behaviour of quantum Heisenberg models

Isaac Goldhirsch, Evgeny Levich, Victor Yakhot

Vinod Mubayi

R. Shanker, R. A. Singh

The anisotropic nearest-neighbour Heisenberg model for the simple cubic lattice has been investigated by interpolating the anisotropy between the Ising and isotropic Heisenberg limits via general spin high-temperature series expansions of the zero-field suspectibility. This is done by estimating the critical temperature (Tc(3)) and the susceptibility exponent γ from the analysis of the series by the Ratio and Pade approximants methods. It is noted that Tc(3) varies with anisotropy while γ is almost the same for the anisotropic system, and a jump in it occurs for the isotropic case in agreement with the universality hypothesis. The effect of anisotropy on the susceptibility is also shown. Further, it is seen that estimates of γ for the two extreme limits agree well with those of previous theoretical as well as experimental investigations. In addition, critical temperatures have been summarised in a relation, and expressions for the magnetisation have been derived.

P. Schlottmann, Kong-Ju-Bock Lee

J. Ricardo de Sousa

D Kim, Colin J. Thompson

For pt.II see ibid., vol.11, p.375 (1978). Exact renormalisation group equations (RGE) are obtained for the d-dimensional n-vector and spin-S Heisenberg versions of Dyson's hierarchical model. In the quantum mechanical case the fixed point and neighbourhood properties of the RGE are shown to be independent of S indicating universality of critical behaviour in spin magnitude. Expansions for critical exponents, analogous to the usual epsilon =4-d expansions, are obtained and the RGE solved numerically to obtain relevant scaling indices. The n to infinity or spherical limit is also discussed and 1/n corrections to critical exponents are calculated to first order in 1/n.