  The prototypical antiferroelectric PbZrO$_3$ has several unsettled questions,
such as the nature of the antiferroelectric transition, possible intermediate
phase and the microscopic origin of the Pbam ground state. Using first
principles, we show that no phonon becomes truly soft at the cubic-to-Pbam
transition temperature, and the order-disorder character of this transition is
clearly demonstrated based on molecular dynamics simulations and potential
energy surfaces. The out-of-phase octahedral tilting is an important degree of
freedom, which can collaborate with other phonon distortions and form a complex
energy landscape with multiple minima. Candidates of the possible intermediate
phase are suggested based on the calculated kinetic barriers between energy
minima, and the development of a first-principles-based effective Hamiltonian.
The use of this latter scheme further reveals that specific bi-linear
interactions between local dipoles and octahedral tiltings play a major role in
the formation of the Pbam ground state, which contrasts with most of the
previous explanations.
