  In this paper, we study the thermodynamic properties of a system of
$D$-components classical Heisenberg spins lying on the vertices of a random
regular graph, with an unconventional first neighbor non-random interaction
$J(\mathbf{S}_i\cdot \mathbf{S}_k)^2$. We can consider this model as a
continuum version of anti-ferromagnetic $D$-states Potts model. We compute the
paramagnetic free energy, using a new approach, presented in this paper for the
first time, based on the replica method. Through the linear stability analysis,
we obtain an instability line on the temperature-connectivity plane that
provides a bound to the appearance of a phase transition. We also argue about
the character of the instability observed.

Disordered Systems and Neural Networks