  All ensembles of statistical mechanics are equivalent in the sense that they
give the equivalent thermodynamic functions in the thermodynamic limit.
However, when investigating microscopic structures in the first-order phase
transition region, one must choose an appropriate statistical ensemble. The
appropriate choice is particularly important when one investigates finite
systems, for which even the equivalence of ensembles does not hold. We propose
a class of statistical ensembles, which always give the correct equilibrium
state even in the first-order phase transition region. We derive various
formulas for this class of ensembles, including the one by which temperature is
obtained directly from energy without knowing entropy. Moreover, these
ensembles are convenient for practical calculations because of good analytic
properties. We also derive formulas which relate statistical-mechanical
quantities of different ensembles, including the conventional ones, for finite
systems. The formulas are useful for obtaining results with smaller finite-size
effects, and for improving the computational efficiency. The advantages of the
squeezed ensembles are confirmed by applying them to the Heisenberg model and
the frustrated Ising model.
