A dynamical model of a quantum measurement process is introduced, where the tested system S, a spin 1 2 , is simultaneously coupled with two apparatuses A and A 0 . Alone, A would measure the component Εz whereas A 0 alone would measure Εx . The apparatus A simulates an Ising magnetic dot involving N spins weakly coupled to a bath of phonons at a temperature lower than the Curie point. Initially in its metastable paramagnetic state, A tends to reach either one of its two equilibrium ferromagnetic states, with magnetization ΓΎm F or Γm F along z, triggered by its interaction with the z-component Εz of S. Likewise, A 0 is coupled to the x-component Εx . The four probabilities of A ΓΎ A 0 depend on the polarizations /s z Γ°0ΓS and /s x Γ°0ΓS of S at the initial time. The counting rates for repeated experiments then determine both /Ε z Γ°0ΓS and /Ε x Γ°0ΓS, although the process cannot be regarded as an ideal measurement. Three apparatuses simultaneously coupled to all three components of S provide full information on the initial density matrix of S through repeated runs. The lack of violation of Bell's inequalities by the indications of the apparatuses is discussed.