  We report that the sample miniaturization of first-order-phase-transition
bulk systems causes a greater degree of supercooling. From a theoretical
perspective, the size effects can be rationalized by considering two
mechanisms: (i) the nucleation is a rare and stochastic event, and thus, its
rate is correlated with the volume and/or surface area of a given sample; (ii)
when the sample size decreases, the dominant heterogeneous nucleation sites
that play a primary role for relatively large samples are annealed out. We
experimentally verified the size effects on the supercooling phenomena for two
different types of strongly correlated electron systems: the transition-metal
dichalcogenide IrTe$_2$ and the organic conductor
$\theta$-(BEDT-TTF)$_2$RbZn(SCN)$_4$. The origin of the size effects considered
in this study does not depend on microscopic details of the material;
therefore, they may often be involved in the first-order-transition behavior of
small-volume specimens.
