Invertible and non-invertible alloy Ising problems

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 {vf}, generating short-range order (SRO), ground states, order-disorder transition temperatures, and structural energy differences. The inverse procedure involves ‘inverting’ the SRO generated from {vj} via inverse-Monte Carlo to obtain a set of pair only interactions { v f } . The physical properties generated from {~vf} are then compared with those from {vf}. We find the following: (i) Inversion of the SRO is possible (even when {vf} contains multibody interactions but { v f { does not). (ii) Nevertheless, the resulting problem interactions { v f } agree with the input interactions {vf} only when the problem is dominated by pair interactions. Otherwise, { v f } are very different from {vf}. (iii) The same SRO pattern can be produced by drastically different sets {vf}. 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 { v f } cannot be used to describe formation enthalpies or two-phase regions of the phase diagram, which depend on G(x).