Spin-spin interaction and magnetic state of 2-D Wigner crystal

It is demonstrated that there is anti-ferromagnetic spin-spin interaction between nearest electrons in the 2D Wigner crystal. This is also valid for the Wigner liquid - the state with destroyed long-range order but preserved short-range one. We calculate the value of the anti-ferromagnetic interaction (both analytically and numerically) and discuss a possible magnetic state of the Wigner crystal. This state can be strongly influenced by the spin-Peierls mechanism.