Invertible and Non-invertible Alloy Ising Models

Abstract

Physical properties of alloys are compared as computed from ``direct'' and ``inverse'' procedures. The direct procedure involves Monte Carlo simulations of a set of local density approximation (LDA)-derived pair and multibody interactions {ν_f}, generating short-range order (SRO), ground states, order- disorder transition temperatures, and structural energy differences. The inverse procedure involves ``inverting'' the SRO generated from {ν_f} via inverse-Monte-Carlo to obtain a set of pair only interactions {\tildeν_f}. The physical properties generated from {\tildeν_f} are then compared with those from {ν_f}. We find that (i) inversion of the SRO is possible (even when {ν_f} contains multibody interactions but {\tildeν_f} does not) but, (ii) the resulting interactions {\tildeν_f} agree with the input interactions {ν_f} only when the problem is dominated by pair interactions. Otherwise, {\tildeν_f} are very different from {ν_f}. (iii) The same SRO pattern can be produced by drastically different sets {ν_f}. Thus, the effective interactions deduced from inverting SRO are not unique. (iv) Inverting SRO always misses configuration-independent (but composition- dependent) energies such as the volume deformation energy G(x); consequently, the ensuing {\tildeν_f} cannot be used to describe formation enthalpies or two-phase regions of the phase diagram, which depend on G(x).