  In this paper, we show that the nonlocal discrete focusing nonlinear
Schr\"odinger (NLS) and nonlocal discrete defocusing NLS equation are gauge
equivalent to the discrete coupled Heisenberg ferromagnet (HF) equation and the
discrete modified coupled HF equation, respectively. Under the continuous
limit, the discrete coupled HF equation and the modified discrete coupled HF
equation lead to the corresponding coupled HF equation and modified coupled HF
equation. This means that the nonlocal focusing and defocusing NLS equations
are gauge equivalent to the coupled HF and coupled modified HF equations. The
solution of the modified coupled HF equation is obtained by using the solution
of nonlocal defocusing NLS equation.
