Low-dimensional quantum antiferromagnets: Criticality and series expansions at zero temperature

Abstract

The theory of scaling for critical points occuring at zero temperature is described. One new exponent, z;- y, is required: this is positive if T is a relevant variable but negative if, as in the random-field Ising model for d>2, a transition for T>0 is controlled by a zero-temperature fixed point. Recent series extrapolation studies by Gelfand, Singh and Huse on the phase transitions and ordering properties of one- and two-dimensional quantal antiferromagnets at zero temperature are reviewed [1–9]. Power series in various parameters about exact Ising and about singlet dimerized ground states have been generated by cluster expansion techniques and quantum perturbation theory carried to orders 5 to 15. Results for phases, phase diagrams, and estimates for critical exponents and other parameters are consistent with analytic analyses [10–12] and experiments [13] and reveal significant new features.