The specific heat (C m ) and optical birefringence (⌬n) for the magnetic percolation threshold system Fe 0.25 Zn 0.75 F 2 are analyzed with the aid of Monte Carlo ͑MC͒ simulations. Both ⌬n and the magnetic energy (U m ) are governed by a linear combination of near-neighbor spin-spin correlations, which we have determined for ⌬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(⌬n)/dT͔ is expected to be proportional to C m since all relevant correlations necessarily have the same temperature dependence. Such a proportionality does not hold for Fe 0.25 Zn 0.75 F 2 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.Measuring the linear optical birefringence (⌬n) in anisotropic, antiferromagnetic crystals undergoing magnetic phase transitions is a powerful way of determining the magnetic specific-heat (C m ) critical behavior. It has been shown 1-3 that the temperature derivative of the optical birefringence ͓d(⌬n)/dT͔ is proportional to C m . In many cases, the birefringence technique has provided the most precise experimental determinations of universal critical behavior parameters 4 in pure and randomly mixed and dilute magnetic Ising systems. For the case of the three-dimensional (dϭ3) random-field Ising model ͑RFIM͒, which applies for a dilute antiferromagnet with an applied field along the ordering direction, birefringence measurements yielded evidence of a phase transition. 5 The advantages of the technique are threefold: the technique is typically much easier to employ than traditional heat pulse techniques; the effects of concentration gradients inevitably present in mixed and dilute crystals can be greatly reduced; 3 and the phonon contributions to the specific heat are greatly suppressed in the birefringence. Since the transition typically varies with concentration in mixed and dilute systems, the critical behavior is often masked by the concentration gradients quenched into the system during growth. The laser beam used in the optical technique can be aligned perpendicular to the gradient, often reducing the gradient effects by an order of magnitude. This has been crucial in the study of random-exchange Ising model ͑REIM͒ and RFIM systems in dϭ2 and 3. The virtual elimination of the phonon background has allowed detailed analysis of the specific heat in dϭ1 and 2 systems. For dϭ2 this has allowed a detailed comparison 6 of the magnetic specific heat of the pure system and the Onsager solution to the dϭ2 Ising model and, for dilute systems, a scaling analysis of the destruction of the phase transition by random fields in the d ϭ2 Ising model...
