Invertible and Non-invertible Alloy Ising Models

TL;DR

This paper compares direct Monte Carlo simulations of alloy properties with inverse procedures that derive interactions from short-range order, revealing limitations in the invertibility and uniqueness of effective interactions.

Contribution

It demonstrates that inverting short-range order to obtain effective interactions is only reliable for pair-dominated systems and highlights the non-uniqueness and limitations of the inverse approach.

Findings

Inversion of SRO is possible but limited to pair interactions.

Effective interactions from inversion are not unique for complex systems.

Inversion misses configuration-independent energies like volume deformation energy.

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 {\nu_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 {\nu_f} via inverse-Monte-Carlo to obtain a set of pair only interactions {\tilde{\nu}_f}. The physical properties generated from {\tilde{\nu}_f} are then compared with those from {\nu_f}. We find that (i) inversion of the SRO is possible (even when {\nu_f} contains multibody interactions but {\tilde{\nu}_f} does not) but, (ii) the resulting interactions {\tilde{\nu}_f} agree with the input interactions {\nu_f} only when the problem is dominated by pair interactions. Otherwise, {\tilde{\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 SRO always misses configuration-independent (but composition- dependent) energies such as the volume deformation energy G(x); consequently, the ensuing {\tilde{\nu}_f} cannot be used to describe formation enthalpies or two-phase regions of the phase diagram, which depend on G(x).