  Complex disordered states - from liquids and glasses to exotic quantum matter
- are ubiquitous in nature. Their key properties include finite entropy,
power-law correlations and emergent organising principles. In spin ice, spin
correlations are determined by an ice rules organising principle that
stabilises a magnetic state with the same zero point entropy as water ice. The
entropy can be manipulated with great precision by a magnetic field: with field
parallel to the trigonal axis one obtains quasi two dimensional kagome ice
which can be mapped onto a dimer model. Here we use a field tilted slightly
away from the trigonal axis to control the dimer statistical weights and
realise the unusual critical behaviour predicted by Kasteleyn. Neutron
scattering on Ho2Ti2O7 reveals pinch point scattering that characterises the
emergent gauge structure of kagome ice; diffuse peaks that shift with field,
signaling the Kasteleyn physics; and an unusual critical point.
