Non-homogeneous mean field picture for spin-glasses

(8)) is based on an exact relation for the renormalized local susceptibility which is valid for all temperatures and external fields in the spin glass phase and has been

vided an analytic mean-field bond model which achieves meV /atom accuracy to the anharmonic free energy of fcc bond lattices with no sampling and negligible computational cost.

If one then represented the environmental life cycle burden by an overall impact assessment value, and the techno-eco- nomic benefits by a cost, expressed over

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We describe athermal packings and their observed geometric phase transitions using equilibrium statistical mechanics and develop a fully microscopic, mean-field theory of the

Under suitable assumptions, if the system at time t = 0 is chaotic (that is to say the particles are independent), this chaos propa- gates as the number of particles goes to

done) unfortunately cannot be avoided. We also notice that for finite size systems the transition is rounded and the correlation length becomes larger than the size of the system at

bending energy of a single membrane and, correspondingly, the free energy of purely undulatory membrane interaction are known to be scale invariant.. The main effect of a gradient