  The specific heat (Cm) and optical birefringence (\Delta n) for the magnetic
percolation threshold system Fe(0.25)Zn(0.75)F2 are analyzed with the aid of
Monte Carlo (MC) simulations. Both \Delta n and the magnetic energy (Um) are
governed by a linear combination of near-neighbor spin-spin correlations, which
we have determined for \Delta n using MC simulations modeled closely after the
real system. Near a phase transition or when only one interaction dominates,
the temperature derivative of the birefringence [{d(\Delta n)}/{dT}] is
expected to be proportional Cm since all relevant correlations necessarily have
the same temperature dependence. Such a proportionality does not hold for
Fe(0.25)Zn(0.75)F2 at low temperatures, however, indicating that neither
condition above holds. MC results for this percolation system demonstrate that
the shape of the temperature derivative of correlations associated with the
frustrating third-nearest-neighbor interaction differs from that of the
dominant second-nearest-neighbor interaction, accurately explaining the
experimentally observed behavior quantitatively.
