Zero temperature solutions of the Edwards-Anderson model in random Husimi Lattices

We solve the Edwards-Anderson model (EA) in different Husimi lattices. We show that, at T=0, the structure of the solution space depends on the parity of the loop sizes. Husimi lattices with odd loop sizes have always a trivial paramagnetic solution stable under 1RSB perturbations while, in Husimi lattices with even loop sizes, this solution is absent. The range of stability under 1RSB perturbations of this and other RS solutions is computed analytically (when possible) or numerically. We compute the free-energy, the complexity and the ground state energy of different Husimi lattices at the level of the 1RSB approximation. We also show, when the fraction of ferromagnetic couplings increases, the existence, first, of a discontinuous transition from a paramagnetic to a spin glass phase and latter of a continuous transition from a spin glass to a ferromagnetic phase.Comment: 20 pages, 10 figures (v3: Corrected analysis of transitions. Appendix proof fixed

Microstructure and Strengthening Mechanisms in an Ultrafine Grained Al-Mg-Sc Alloy Produced by Powder Metallurgy

Additions of Sc to an Al-Mg matrix were investigated, paying particular attention to the influence of Al3Sc precipitates and other dispersoids, as well as grain size, on mechanical behavior. Prior studies have shown that Sc significantly increases the strength of coarse-grained Al-Mg alloys. Prompted by these findings, we hypothesized that it would be of fundamental and technological interest to study the behavior of Sc additions to an ultrafine-grained (UFG) microstructure (e.g., 100\u27s nm). Accordingly, we investigated the microstructural evolution and mechanical behavior of a cryomilled ultrafine grained Al-5Mg-0.4Sc (wt pct) and compared the results to those of an equivalent fine-grained material (FG) produced by powder metallurgy. Experimental materials were consolidated by hot isostatic pressing (HIP\u27ing) followed by extrusion or dual mode dynamic forging. Under identical processing conditions, UFG materials generate large Al3Sc precipitates with an average diameter of 154 nm and spaced approximately 1 to 3 μm apart, while precipitates in the FG materials have a diameter of 24 nm and are spaced 50 to 200 nm apart. The strengthening mechanisms are calculated for all materials and it is determined that the greatest strengthening contributions for the UFG and FG materials are Mg-O/N dispersion strengthening and precipitate strengthening, respectively