  Background: Quantum Chromodynamics is expected to have a phase transition in
the same static universality class as the 3D Ising model and the liquid-gas
phase transition. The properties of the equation of state, the transport
coefficients, and especially the location of the critical point are under
intense theoretical investigation. Some experiments are underway, and many more
are planned, at high energy heavy ion accelerators. Purpose: Develop a model of
the thermal conductivity, which diverges at the critical point, and use it to
study the impact of hydrodynamic fluctuations on observables in high energy
heavy ion collisions. Methods: We apply mode coupling theory, together with a
previously developed model of the free energy that incorporates the critical
exponents and amplitudes, to construct a model of the thermal conductivity in
the vicinity of the critical point. The effect of the thermal conductivity on
correlation functions in heavy ion collisions is studied in a boost invariant
hydrodynamic model via fluctuations, or noise. Results: We find that the closer
a thermodynamic trajectory comes to the critical point the greater is the
magnitude of the fluctuations in thermodynamic variables and in the 2-particle
correlation functions in momentum space. Conclusions: It may be possible to
discern the existence of a critical point, its location, and thermodynamic and
transport properties near to it in heavy ion collisions using the methods
developed here.
