One-dimensional spin-1/2 Heisenberg antiferromagnet in a weak external magnetic field

The one dimensional spin-1/2 Heisenberg antiferromagnet in a weak magnetic field h is studied using the bosonization method. We derive a set of renormalization group equations. The fixed point is reached when the field is scaled to the value at which the system is quarter-filled. As the magnetic field varies, a continuum line of fixed points is formed. We compute the uniform longitudinal susceptibility ${\chi }_z(h)$. The singular behavior of ${\chi }_z(h)$ as $h\to 0$ is found to be contained in $1\mathrm{/}\ln (h_o\mathrm{/}h)$ with $h_o$ a non-universal constant. The spin-spin correlations in the magnetic field are calculated.