  Critical behavior is very common in many fields of science and a wide variety
of many-body systems exhibit emergent critical phenomena. The beauty of
critical phase transitions lies in their scale-free properties, such that the
temperature dependence of physical parameters of systems differing at the
microscopic scale can be described by the same generic power laws. In this work
we establish the critical properties of the antiferromagnetic phase transition
in artificial square ice, showing that it belongs to the two-dimensional Ising
universality class, which extends the applicability of such concepts from
atomistic to mesoscopic magnets. Combining soft x-ray resonant magnetic
scattering experiments and Monte Carlo simulations, we characterize the
transition to the low temperature long range order expected for the artificial
square ice system. By measuring the critical scattering, we provide direct
quantitative evidence of a continuous magnetic phase transition, obtaining
critical exponents which are compatible with those of the two-dimensional Ising
universality class. In addition, by varying the blocking temperature relative
to the phase transition temperature, we demonstrate its influence on the
out-of-equilibrium dynamics due to critical slowing down at the phase
transition.
