parameter $x=\frac{t}{U}$ $(x\ll 1)$. This idea (cf Refs \[31,32\]) consists in replacing ”difficult physics” connected with the model by ”difficult mathematics” obtained by a laborious expansion with respect to $x.$ Different methods connected with this problem have been applied as e.g. the perturbation expansion (see Refs \[18\], \[21\]), canonical transformation (see Refs \[9\], \[12\], \[17\], \[22\], \[23\]) or ab initio derivations (see Refs \[25\], \[28-30\]). Most of the methods, leading to the $%
t-J$ model (or generalized $t-J$ model) are also summarized in Refs \[27\], \[4\].

The goal of the present paper is just to show that we can take another, nonperturbative way. In the first step we divide the crystal lattice into a set of interacting dimers. In other words, we can rewrite the Hubbard Hamiltonian (1) for the sc lattice (see Fig. 1) in the equivalent form [^2]:

$$\begin{array}{ll}
H= & \sum\limits_IH_I^d-t\sum\limits_{I,\sigma }(c_{I,2,\sigma
}^{+}c_{I+1,1,\sigma }+c_{I+1,1,\sigma }^{+}c_{I,2,\sigma }) \\
& -t\sum\limits_{I\neq J,\sigma }(c_{I,1,\sigma }^{+}c_{J,1,\sigma
}+c_{I,2,\sigma }^{+}c_{J,2,\sigma })
\end{array}$$

where

$$H_I^d=-t\sum\limits_{\sigma} (c_{I,1,\sigma }^{+}c_{I,2,\sigma
}+c_{I,2,\sigma }^{+}c_{I,1,\sigma })+U(n_{I,1,\uparrow }n_{I,1,\downarrow
}+n_{I,2,\uparrow }n_{I,2,\downarrow }).$$

The indices $I$ and $J$ enumerate the dimers and $H_I^d$ is the dimer Hamiltonian. The second term in (4) describes the hopping between nearest dimers in the $z$-direction, the third 