  The phase-transition sequence of a ferroelectric perovskite such as BaTiO_3
can be simulated by computing the statistical mechanics of a first-principles
derived effective Hamiltonian [Zhong, Vanderbilt and Rabe, Phys. Rev. Lett. 73,
1861 (1994)]. Within this method, the effect of an external pressure (in
general, of any external field) can be studied by considering the appropriate
"enthalpy" instead of the effective Hamiltonian itself. The legitimacy of this
approach relies on two critical assumptions that, to the best of our knowledge,
have not been adequately discussed in the literature to date: (i) that the
zero-pressure relevant degrees of freedom are still the only relevant degrees
of freedom at finite pressures, and (ii) that the truncation of the Taylor
expansion of the energy considered in the effective Hamiltonian remains a good
approximation at finite pressures. Here we address these issues in detail and
present illustrative first-principles results for BaTiO_3. We also discuss how
to construct effective Hamiltonians in cases in which these assumptions do not
hold.
