  We show that, at the critical temperature, there is a class of Lee-Yang zeros
of the partition function in a general scalar field theory, which location
scales with the size of the system with a characteristic exponent expressed in
terms of the isothermal critical exponent $\delta$. In the thermodynamic limit
the zeros belonging to this class condense to the critical point {\zeta}=1 on
the real axis in the complex fugacity plane while the complementary set of
zeros (with Re {\zeta} < 1) covers uniformly the unit circle. Although the
aforementioned class degenerates to a single point for an infinite system, when
the size is finite it dominates in the partition function and determines the
self-similar structure (fractal geometry, scaling laws) of the critical system.
This property opens up the perspective to formulate finite-size scaling theory
in effective QCD, near the chiral critical point, in terms of the location of
Lee-Yang zeros.
