Topologically correct phase boundaries and transition temperatures for Ising Hamiltonians via self-consistent coarse-grained cluster-lattice models

Tan, Teck Leong; Johnson, Duane D.

doi:10.1103/physrevb.83.144427

Cited by 11 publications

(14 citation statements)

References 46 publications

(74 reference statements)

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“…The problem simplifies in lattice models where the infinite system can be modeled by a finite cluster of lattice sites. In classical models which will be discussed in the present Letter the cluster partition function can be calculated exactly to all orders in Hamiltonian and with a suitable embedding of the cluster into the infinite system remarkably accurate results can be obtained with the use of small clusters [1,2,3,4]. The cluster approximation is systematic in the sense that it can be indefinitely improved by enlarging the cluster size, so in principle it presents a viable alternative to the series expansions as a general approach to many-body problems with strong interactions.…”

Section: Introductionmentioning

confidence: 93%

“…The cluster approximation is systematic in the sense that it can be indefinitely improved by enlarging the cluster size, so in principle it presents a viable alternative to the series expansions as a general approach to many-body problems with strong interactions. The main drawback of the cluster approach is that computationally accessible dimensions of the clusters are limited so it is impossible to adequately treat very long-range correlations [2,4] which are indispensable in the description of the second order phase transitions and critical phenomena [5].…”

Section: Introductionmentioning

confidence: 99%

“…Taking into account that some non-universal quantities, such as the critical temperatures, can be calculated with good accuracy within the cluster method [2,4], in the spirit of the RG approach it would be natural to use some cluster technique to account for the short-range fluctuations and resort to RG only for the treatment of the long-range ones. A step in realization of this approach was made in [10] where the authors have succeeded in calculating a magnetization curve and several critical temperatures in good agreement with the best known values.…”

Section: Introductionmentioning

confidence: 99%

“…This, however, was achieved with the introduction of arbitrary parameters into the calculations which casts doubts on the predictive abilities of the approach. Besides, no recipe was given of incorporation into the RG procedure of the notion of the effective medium which is central in the existing cluster approaches [2,3,4] was not introduced in the in the RG scheme in [10].…”

Section: Introductionmentioning

confidence: 99%

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Effective medium approach in the renormalization group theory of phase transitions

Tokar

2019

Preprint

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An effective medium approach similar to the coherent potential approximation (CPA) in the theory of disordered alloys and to the DMFT has been extended to the renormalization group equations in the local potential approximation (LPA). Non-universal characteristics of the second order phase transitions such as the critical temperatures and critical amplitudes have been calculated in good agreement with the best known estimates. A possibility of cluster extension of the LPA to improve its accuracy and to make the approach systematic and self-contained has been discussed. A qualitative explanation of the discrepancy between theoretical value of the critical exponent β and recent experimental data on ordering in beta brass by the influence of non-universal contributions has been suggested.

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Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effective medium approach in the renormalization group theory of phase transitions

Tokar

2019

Preprint

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“…The correction is historically called the Onsager cavity field correction [35], which renormalizes the thermodynamic excitation energies to conserve the diffuse intensity over the Brillouin zone. Although not commonly used as a more proper mean-field theory, this single-site fix to mean-field theory corrects the topological error in mean-field phase diagrams, such as Bragg-Williams (Ising) models [36].…”

Section: Computational Detailsmentioning

confidence: 99%

Atomic short-range order and incipient long-range order in high-entropy alloys

2015

Self Cite

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Within density-functional theory, we apply an electronic-structure-based thermodynamic theory to calculate short-ranged order (SRO) in homogeneously disordered substitutional N-component alloys, and its electronic origin. Using the geometric properties of an (N−1) simplex that describes the Gibbs (compositional) space, we derive the analytic transform of the SRO eigenvectors that provides a unique description of high-temperature SRO in N-component alloys and the incipient low-temperature long-range order. We apply the electronic-based thermodynamic theory and the new general analysis to ternaries (A1 CuNi-Zn and A2 Nb-Al-Ti) for validation, and then to quinary Al-Co-Cr-Fe-Ni high-entropy alloys for predictive assessment. Within density-functional theory, we apply an electronic-structure-based thermodynamic theory to calculate short-ranged order (SRO) in homogeneously disordered substitutional N -component alloys, and its electronic origin. Using the geometric properties of an (N − 1) simplex that describes the Gibbs (compositional) space, we derive the analytic transform of the SRO eigenvectors that provides a unique description of high-temperature SRO in N -component alloys and the incipient low-temperature long-range order. We apply the electronic-based thermodynamic theory and the new general analysis to ternaries (A1 Cu-Ni-Zn and A2 Nb-Al-Ti) for validation, and then to quinary Al-Co-Cr-Fe-Ni high-entropy alloys for predictive assessment. Keywords Materials Science and Engineering

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Computation of Diffuse Intensities in Alloys

Johnson

Pinski

Staunton

2012

Characterization of Materials

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Diffuse intensities in alloys are measured by a variety of techniques, such as x‐ray,electron and neutron scattering. Above a structural phase transformation boundary, typically in the solid‐solution phasewhere most materials processing takes place, the diffuse intensities yield valuable information regarding analloy's tendency to order. This has been a main stay characterization technique for binary alloys for over a half a century. Although multicomponent metallic alloys are the most technologically important, they also pose a great experimental and theoretical challenge. For this reason, a vast majority of experimental and theoretical effort has been on binary systems, and most investigated “ternary” systems are either limited to a small percentage of ternary solute (say, to investigate electron‐per‐atom effects) or they are pseudo‐binary systems. This article discusses an electronic‐based theoretical method for calculating the structural ordering in multicomponent alloys and understanding the electronic origin for this chemical ordering behavior. This theory is based on the ideas of concentration waves using a modern electronic‐structure method. We give examples that show how we determined the electronic origin behind the unusual ordering behavior in a few binary and ternary alloy systems that were not understood prior to our work. The theoretical approach is compared to other complimentary techniques for completeness. In addition, some details are given about the theory and its underpinnings. In particular, it has been explained only recently how important a proper representation of charge density is when applying various approximations to represent ordered and, especially, disordered alloys, which we provide some examples.

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Topologically correct phase boundaries and transition temperatures for Ising Hamiltonians via self-consistent coarse-grained cluster-lattice models

Cited by 11 publications

References 46 publications

Effective medium approach in the renormalization group theory of phase transitions

Effective medium approach in the renormalization group theory of phase transitions

Atomic short-range order and incipient long-range order in high-entropy alloys

Computation of Diffuse Intensities in Alloys

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