= Magnetization of the quantum XX chain
{title2=$m_z=\pi^{-1}\arcsin(h/J),\quad0\le h\le J$}
For exchange $J>0$, the <Jordan–Wigner transformation> gives a band $\epsilon_k=h-J\cos k$. At zero <temperature>, negative-energy states form a filled interval $|k|<\arccos(h/J)$. Since each <fermion> decreases total <magnetization> by one, the thermodynamic <magnetization> per site is $1/2-\arccos(h/J)/\pi$. It saturates at $1/2$ for $h\ge J$. A finite ring instead has discrete level crossings and parity-dependent <momentum> grids.
Back to article page
