Scaling regimes, crossovers, and lattice corrections in two-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 T≲JS, where J is the exchange coupling, c approaches its known T=0 values, ${\mathit{c}}_0$. This nonuniversal lattice effect is caused by the quantum nature of spin, and is therefore not captured by the quantum nonlinear σ model.