  Phase transitions and critical phenomena are among the most intriguing
phenomena in nature and their renormalization-group theory is one of the
greatest achievements of theoretical physics. However, the predictions of the
theory above an upper critical dimension $d_c$ seriously disagree with reality.
In addition to its fundamental significance, the problem is also of practical
importance because both complex systems with spatial or temporal long-range
interactions and quantum phase transitions can substantially lower $d_c$. The
extant scenarios built on a dangerous irrelevant variable (DIV) to resolve the
problem introduce two sets of critical exponents and even two sets of scaling
laws whose origin is obscure. Here, we consider the DIV from a different
perspective and clearly unveil the origin of the two sets of exponents and
hence the intrinsic inconsistency in those scenarios. We then develop an
effective-dimension theory in which critical fluctuations and system volume are
fixed at an effective dimension by the DIV. This enables us to account for all
the extant results consistently. A novel asymptotic finite-size scaling
behavior for a correlation function together with a new anomalous dimension and
its associated scaling law is also derived.
