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.
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