Critical equation of state of randomly dilute Ising systems

We determine the critical equation of state of three-dimensional randomly dilute Ising systems- i.e., of the random-exchange Ising universality class. We first consider the small-magnetization expansion of the Helmholtz free energy in the high-temperature phase. Then, we apply a systematic approximation scheme of the equation of state in the whole critical regime, which is based on polynomial parametric representations matching the small-magnetization expansion of the Helmholtz free energy and satisfying a global stationarity condition. These results allow us to estimate several universal amplitude ratios, such as the ratio A(+)/A(-) of the specific-heat amplitudes. Our best estimate A(+)/A(-)=1.6(3) is in good agreement with experimental results on dilute uniaxial antiferromagnets.