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 { v 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 { v j } via inverse-Monte Carlo to obtain a set of pair only interactions { v ̃ f} . The physical properties generated from {~ v f } are then compared with those from { v f }. We find the following: (i) Inversion of the SRO is possible (even when { v f } contains multibody interactions but { v ̃ f{ does not). (ii) Nevertheless, the resulting problem interactions { v ̃ f} agree with the input interactions { v f } only when the problem is dominated by pair interactions. Otherwise, { v ̃ f} are very different from { v f }. (iii) The same SRO pattern can be produced by drastically different sets { v 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 { v ̃ f} cannot be used to describe formation enthalpies or two-phase regions of the phase diagram, which depend on G( x).