Effective classical Hamiltonians for spin systems: A closed form with quantum spin-wave effects

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Thermodynamic properties of any quantum spin system can be described by the formally exact, although in general intractable, effective classical Hamilton function H. Here we obtain an explicit form of H which applies at T << J S², where J is the exchange and S in the spin value, and incorporates quantum effects at the level of the spin-wave theory (SWT). For a quantum Hamiltonian H of Heisenberg form, H is also Heisenberg but with a long-range effective exchange Jijeff, which is the price for including quantum effects. For three-dimensional magnets, classical SWT with H yields the same results as quantum SWT for the original system, in the antiferromagnetic case with the 1/S correction to the ground-state energy.