SCALING REGIMES, CROSSOVERS, AND LATTICE CORRECTIONS IN 2-DIMENSIONAL HEISENBERG ANTIFERROMAGNETS

We study scaling behavior in two-dimensional, square lattice, S=1/2 and S=1 Heisenberg antiferromagnets using the data on full q dependences of the equal-time structure factor and the static susceptibility, calculated through high-temperature series expansions. We also carry out comparisons with a model of two coupled S=1/2 Heisenberg planes with the interlayer exchange coupling tuned to the T=0 critical point (two-plane model hereafter). For both S=1/2 and S=1 models, we separately determine the spin-wave velocity c and mass m=c/ξ, in addition to the correlation length, ξ, and find that c is temperature dependent; only for temperatures below TJS, where J is the exchange coupling, c approaches its known T=0 values, c0. This nonuniversal lattice effect is caused by the quantum nature of spin, and is therefore not captured by the quantum nonlinear σ model. Despite this temperature dependence of the spin-wave velocity, full q and ω dependences of the dynamical susceptibility χ(q,ω) agree with those of the universal scaling function, computable for the σ model, for temperatures up to T0∼0.6c0/a, and their further analysis leads us to the inference that below T0 the S=1 model is in the renormalized classical (RC) regime, the two-plane model is in the quantum critical (QC) regime in agreement with earlier work, and the S=1/2 model exhibits a RC-QC crossover, centered around crossover and for the two-plane model at all T=0.55J. In particular, for the S=1/2 model above the RC-QC temperatures where calculated, the obtained spin-wave mass m=c/ξ is in excellent agreement with the known universal QC prediction, m1.04T. In contrast, for the S=1/2 model below the RC-QC crossover, and for the S=1 model at all temperatures, the behavior agrees with the exact RC expression. for all three models, nonuniversal behavior occurs above T∼0.6c0/a. Our results strongly support the conjecture by Chubukov and Sachdev that the S=1/2 model is close enough to the T=0 critical point to exhibit QC behavior at intermediate temperatures. © 1995 The American Physical Society.