  Spontaneous, collective ordering of electronic degrees of freedom leads to
second-order phase transitions that are characterized by an order parameter.
The notion "hidden order" (HO) has recently been used for a variety of
materials where a clear phase transition occurs to a phase without a known
order parameter. The prototype example is the heavy-fermion compound URu2Si2
where a mysterious HO transition occurs at 17.5K. For more than twenty years
this system has been studied theoretically and experimentally without a firm
grasp of the underlying physics. Using state-of-the-art density-functional
theory calculations, we provide here a microscopic explanation for the HO. We
identify the Fermi surface "hot spots" where degeneracy induces a Fermi surface
instability and quantify how symmetry breaking lifts the degeneracy, causing a
surprisingly large Fermi surface gapping. As mechanism for the HO we propose
spontaneous symmetry breaking through collective antiferromagnetic moment
excitations.
