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There is a recently discovered formulation of the multidimensionalconsistency integrability condition for lattice equations, calledconsistency-around-a-face-centered-cube(CAFCC), which is applicable toequations defined on a vertex and its four nearest neighbours on the squarelattice. This paper introduces a method of deriving Lax matrices for theequations which satisfy CAFCC. This method gives novel Lax matrices for suchequations, which include previously known equations of discrete Toda-, orLaplace-type, as well as newer equations which have only appeared in thecontext of CAFCC.

Lax matrices for lattice equations which satisfy consistency-around-a-face-centered-cube