Simplified tetrahedron equations: Fermionic realization

The natural generalization of the (two-dimensional) Yang-Baxter equations to three dimensions is known as the Zamolodchikov's tetrahedron equations. We consider a simplified version of these equations which still ensures the commutativity of the transfer matrices with different spectral parameters and we present a family of free fermionic solutions. (c) 2005 Elsevier B.V. All rights reserved.