Invertible and Non-Invertible Alloy Ising Problems

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 {.nu.f}, generating short-range order (SRO), ground states, order--disorder transition temperatures, and structural energy differences. The inverse procedureinvolves 'inverting' the SRO generated from {.nu.j} via inverse-Monte Carlo to obtain a set of pair only interactions {~.nu.f}. The physical properties generated from {~.nu.f} are then compared with those from {.nu.f}. We find the following: (i) Inversion of the SRO is possible (even when {.nu.f} contains multibody interactions but {~.nu.f} does not). (ii) Nevertheless, the resulting probleminteractions {`.nu.f} agree with the input interactions {.nu.f} only when the problem is dominated by pair interactions. Otherwise, {~.nu.f} are very different from {.nu.f}. (iii) The same SRO pattern can be produced by drastically different sets {.nu.f}. Thus, the effective interactions deduced from inverting SRO are not unique. (iv) Inverting interactions deduced from inverting SRO are notunique. (iv) Inverting SRO always misses configuration-independent (but composition-dependent) energies such as the volume deformation energy G(x); consequently, the ensuing {~.nu.f} cannot be used to describe formation enthalpies or two-phase regions of the phase diagram, which depend on G(x).