  As first asserted by Y. Imry and S-K Ma, the famed discontinuity of the
magnetization as function of the magnetic field in the two dimensional Ising
model is eliminated, for all temperatures, through the addition of quenched
random magnetic field of uniform variance, even if that is small. This
statement is quantified here by a power-law upper bound on the decay rate of
the effect of boundary conditions on the magnetization in finite systems, as
function of the distance to the boundary. Unlike exponential decay which is
only proven for strong disorder or high temperature, the power-law upper bound
is established here for all field strengths and at all temperatures, including
zero, for the case of independent Gaussian random field. Our analysis proceeds
through a streamlined and quantified version of the Aizenman-Wehr proof of the
Imry-Ma rounding effect.
