Phase transitions in quasi-one-dimensional magnetic structures: Quantum effects

Semiclassical spin-wave theory leads to a low-temperature ($k_{B}T\ll J$) static correlation function for a one-dimensional Heisenberg antiferromagnet having the approximate form $〈S_x\mathrm{}\left(0\right)\mathrm{}{S}_x\mathrm{}\left(r\right)\mathrm{}〉 r^{-\lambda }{e}^{\frac{-r}{\xi }}$, where $\xi \mathrm{}\left(T\right)\mathrm{}$ is the classical correlation length and $\lambda =2\mathrm{}{\left(\pi S\right)}^{-1}$ ($S$ is the spin quantum number) is the quantum correction. This leads to a three-dimensional Néel temperature for exchange-coupled chains (with interchain exchange $J_{\perp }$), $T_N\propto {\left(\frac{J_{\perp }}{J}\right)}^{\frac{1}{(2-\lambda )}}$. The magnetic field dependence of the quantum exponent $\lambda$ is shown to lead to an important field dependence for $T_N$.