Alonso, J. L.Fernández Pérez, Luis AntonioGuinea, F.Laliena, V.Martín Mayor, Víctor2023-06-202023-06-202011-02-011098-012110.1103/PhysRevB.63.054411https://hdl.handle.net/20.500.14352/42572© 2001 The American Physical Society. We are thankful for helpful conversations to L. Brey, J. Fontcuberta, G. Gómez-Santos, C. Simon, J. M. de Teresa, and especially to R. Ibarra and V. S. Amaral. V.M.-M. was partially supported by MEC. We acknowledge financial support from Grant Nos. PB96-0875, AEN97-1680, AEN97- 1693, AEN97-1708, AEN99-0990 (MEC, Spain), and (07N/0045/98) (C. Madrid).It has been recently shown that the double exchange Hamiltonian, with weak antiferromagnetic interactions, has a richer variety of first- and second-order transitions than previously anticipated, and that such transitions are consistent with the magnetic properties of manganites. Here we present a thorough discussion of the variational mean-field approach that leads to these results. We also show that the effect of the Berry phase turns out to be crucial to produce first-order paramagnetic-ferromagnetic transitions near half filling with transition temperatures compatible with the experimental situation. The computation relies on two crucial facts: the use of a mean-field ansatz that retains the complexity of a system of electrons with off-diagonal disorder, not fully taken into account by the mean-field techniques, and the small but significant antiferromagnetic superexchange interaction between the localized spins.engjournal articlehttp://doi.org/10.1103/PhysRevB.63.054411http://journals.aps.orgopen access53Spectral moments methodDiluted ising-modelPhase-separationColossal magnetoresistanceFerromagnetic manganitesManganese perovskitesCritical exponentsElectronic modelsDoped manganiesSpin dynamics.Física (Física)Física-Modelos matemáticos22 Física