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The possibility of cooling solid He3 by adiabatic magnetization is discussed using the antiferromagnetic nearest-neighbor spin-½ Heisenberg linear chain as a reference system. The lack of a phase transition is not important in this discussion since the locus of maximum cooling generally lies outside (i.e., is unrelated to) the T−H phase boundary, contrary to previous predictions using mean-field and spin-wave theories. Exact calculations on linear chains demonstrate a potentially useful degree of equilibrium cooling. The results are in qualitative agreement with earlier spin-wave arguments, although the details of the energy spectrum are more complicated than is assumed in spin-wave theory.