  We consider an infinite harmonic chain of charged particles submitted to the
action of a magnetic field of intensity $B$ and subject to the action of a
stochastic noise conserving the energy. In arXiv:0809.0177 and arXiv:1402.2988
it has been proved that if $B=0$ the transport of energy is described by a
$3/4$-fractional diffusion while it has been proved in arXiv:1808.01040 that if
$B\ne 0$ it is described by a $5/6$-fractional diffusion. In this paper we
quantify the intensity of the magnetic field necessary to pass from one regime
to the other one. We also describe the transition mechanism to cross the two
different phases.
