中文摘要：

对于离散的修正海森堡铁磁链方程，相关研究表明若将其自旋矢量用闵可夫斯基空间中的离散曲线的单位矢量代替，则可给出与其几何等价的可积微分一差分方程．通过规范变换具体证明了相关的离散修正海森堡铁磁链方程与其几何等价的可积微分一差分方程之间具有规范等价性关系．

英文摘要：

For the discrete integrable modified Heisenberg ferromagnet equation, it is known that the geometric equivalent integrable differential-difference equation can be obtained by identifying the spin vector with the unit vectors of discrete curve in Minkowski space. In this paper, we prove that there is the gauge equivalence between the discrete modified Heisenberg ferromagnet equation and the corresponding geometric equivalent differential-difference equation.