Summary
The spin glass phase of a system of Ising spins interacting via the RKKY interaction is investigated at a mean-field level. The results around the transition temperature are at sharp variance with those previously found by other authors and suggest a first-order transition. The static susceptibility is found to deviate from Fischer's predictions. A test of the validity of scaling predictions is also performed.
Riassunto
La fase di ≪spin glass≫ di un sistema di spin di Ising interagenti tramite un'interazione del tipo RKKY è studiata in campo medio. I risultati nell'intorno della temperatura di transizione sono in netto contrasto con quelli in precedenza trovati da altri autori e suggeriscono una transizione del prim'ordine. Si trova che la suscettività statica devia dalle predizioni di Fischer. Si effettua anche una verifica della validità delle leggi di scala.
Резюме
На уровне среднего поля исследуется фаза спинового стекла для системы спинов Изинга, взаимодействующих через RKKY взаумодействие. Полученные результаты для температуры перехода сильно отличаются от результатов, полученных ранее другими авторами, и предполагают переход первого порядка. Обнаружено, что статическая восприимчивость отличается от предсказаний Фишера. Также проводится проверка справедливости предсказаний подобия.
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Equation (2) was derived by using, as in the rest of the literature, a short-distance cut-offd on the interaction, chosen here for simplicity to be such that 2k F d∼1, whence the lower bounds of integration in eqs. (3) and (4). One might dispense from the cut-off by using the full form of the RKKY interaction,i.e. by writing (x cosx−sinx)/x 4 in place of (cosx)/x 3 in the above equations and setting the lower bounds of integration to zero. However, the original physical problem being formulated on a lattice, the use of a cut-off of the order of the lattice parameter seems to be more natural.
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In a cut-off-free treatment (see footnote (15)) Equation (2) was derived by using, as in the rest of the literature, a short-distance cut-offd on the interaction, chosen here for simplicity to be such that 2k F d∼1, whence the lower bounds of integration in eqs. (3) and (4). One might dispense from the cut-off by using the full form of the RKKY interaction,i.e. by writing (x cosx−sinx)/x 4 in place of (cosx)/x 3 in the above equations and setting the lower bounds of integration to zero. However, the original physical problem being formulated on a lattice, the use of a cut-off of the order of the lattice parameter seems to be more natural. one would instead obtain Γ(0)=−1.
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Corbelli, G., Lovecchio, G. & Morandi, G. Order parameter and static susceptibility of spin glasses in mean-field theory. Il Nuovo Cimento D 1, 225–234 (1982). https://doi.org/10.1007/BF02450081
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DOI: https://doi.org/10.1007/BF02450081