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Effect of Short-Range Fluctuations on Thermodynamic and Resistive Properties: The case of Ising Order

We consider the effects of the non-local Ising-like "core spin" correlations on the order-parameter fluctuation contribution to the resistivity and thermodynamics of metals showing Ising-like order at finite temperature. We employ the well-known cluster-variation method, and present explicit results in the pair approximation for short-range order. Our calculation generalizes earlier works, where such effects were considered in the mean-field (Ornstein-Zernicke) approximation. The mean-field (MF) transition temperature T_{c}^{MF}, is corrected to O(1/d), and the effect of the Ising spin fluctuations on the $dc$ resistivity and magnetothermal responses is analyzed in detail. The method can be applied straightforwardly to lattices in arbitrary d, and, as an appealing feature, it reproduces the exact correlation length and T_{c}^{1d}=0 for the 1d Ising model. We apply our results for two interesting physical cases: (i) the double-exchange model with J_{H}>>t, where the core-spins can be approximated quite well by Ising spins, and (ii) a model of band electrons coupled to a {\it localized} subsystem which undergoes a nematic ordering transition coupled to an appropriate structural transition.