Why NPT ensemble is used for solid state phase transitions? In Monte Carlo simulations of solid state phase transitions, why often Isobaric Isothermal ensemble (NPT) is used ? Why not NVT ?
Here, N is number of atoms, P is pressure, T is temperature and V is volume.
 A: A simple example where the NPT ensemble would be necessary is a phase transition between two different crystal structures. Iron, for example, has both BCC and FCC regions in its phase diagram. This phase transition comes with an 8-9% change in density, so the simulation cell needs to be able to change its volume to allow this to occur. The Clausius–Clapeyron relation tells us that for a first-order phase transition
$\frac{dP}{dT} = \frac{L}{T\Delta v}$
The slope of the phase-coexistence line on the PT phase diagram is proportional to the latent heat of the transition ($L$)  and inversely to the temperature ($T$) and change in specific volume ($\Delta v$). (check out the Wikipedia page).
However, even if there is no difference in density between the initial and final crystal structures, the path between them is likely to involve structures which are less dense, and the simulation needs to accommodate that. Look up the Parinello-Rahman barostat to see how this is typically done.
That's the simple, intuitive answer. However, to do Monte Carlo simulations of a phase transition correctly you need to think about the thermodynamics very carefully. 
A really great resource is the book "Understanding Molecular Simulation" by Frenkel. I would also recommend reading the following paper: 
Frenkel, D. (2013). Simulations: The dark side. The European Physical Journal Plus, 128(1), 1–21
