Local Symmetry Research Articles

Dichotomous dynamics of magnetic monopole fluids

A recent advance in the study of emergent magnetic monopoles was the discovery that monopole motion is restricted to dynamical fractal trajectories [J. N. Hallén et al., Science 378, 1218 (2022)], thus explaining the characteristics of magnetic monopole noise spectra [R. Dusad et al., Nature 571, 234 (2019); A. M. Samarakoon et al., Proc. Natl. Acad. Sci. U.S.A. 119, e2117453119 (2022)]. Here, we apply this novel theory to explore the dynamics of field-driven monopole currents, finding them composed of two quite distinct transport processes: initially swift fractal rearrangements of local monopole configurations followed by conventional monopole diffusion. This theory also predicts a characteristic frequency dependence of the dissipative loss angle for AC field-driven currents. To explore these novel perspectives on monopole transport, we introduce simultaneous monopole current control and measurement techniques using SQUID-based monopole current sensors. For the canonical material Dy2Ti2O7, we measure [Formula: see text], the time dependence of magnetic flux threading the sample when a net monopole current [Formula: see text] is generated by applying an external magnetic field [Formula: see text] These experiments find a sharp dichotomy of monopole currents, separated by their distinct relaxation time constants before and after t ~[Formula: see text] from monopole current initiation. Application of sinusoidal magnetic fields [Formula: see text] generates oscillating monopole currents whose loss angle [Formula: see text] exhibits a characteristic transition at frequency [Formula: see text] over the same temperature range. Finally, the magnetic noise power is also dichotomic, diminishing sharply after t ~[Formula: see text]. This complex phenomenology represents an unprecedented form of dynamical heterogeneity generated by the interplay of fractionalization and local spin configurational symmetry.

Anatomy of Hidden Dzyaloshinskii-Moriya Interactions and Topological Spin Textures in Centrosymmetric Crystals.

The Dzyaloshinskii-Moriya interaction (DMI) is understood to be forbidden by the symmetry of centrosymmetric systems, thus restricting the candidate types for investigating many correlated physical phenomena. Here, we report the hidden DMI existing in centrosymmetric magnets driven by the local inversion symmetry breaking of specific spin sublattices. The opposite DMI spatially localized on the inverse spin sublattice favors the separated spin spiral with opposite chirality. Furthermore, we elucidate that hidden DMI widely exists in many potential candidates, from the first-principles calculations on the mature crystal database. Interestingly, novel topological spin configurations, such as the anti-chirality-locked merons and antiferromagnetic-ferromagnetic meron chains, are stabilized as a consequence of hidden DMI. Our understanding enables the effective control of DMI by symmetry operations at the atomic level and enlarges the range of currently useful magnets for topological magnetism.

Linearly Polarized Broadband Emission and Multi-Wavelength Lasing in Solution-Processed Quantum Dots.

A miniature laser with linear polarization is a long sought-after component of photonic integrated circuits. In particular, for multi-wavelength polarization lasers, it supports simultaneous access to multiple, widely varying laser wavelengths in a small spatial region, which is of great significance for advancing applications such as optical computing, optical storage, and optical sensing. However, there is a trade-off between the size of small-scale lasers and laser performance, and multi-wavelength co-gain of laser media and multi-cavity micromachining in the process of laser miniaturization remain as significant challenges. Herein, room-temperature linearly polarized multi-wavelength lasers in the visible and near-infrared wavelength ranges are demonstrated, by fabricating random cavities scattered with silica in an Er-doped Cs2Ag0.4Na0.6In0.98Bi0.02Cl6 double-perovskite quantum dots (QDs) gain membrane. By regulating the local symmetry and enabling effective energy transfer in nanocrystals, multi-wavelength lasers with ultra-low thresholds are achieved at room temperature. The maximum degree of polarization reaches 0.89. With their advantages in terms of miniaturization, ultra-low power consumption, and adaptability for integration, these lasers offer a prospective light source for future photonic integrated circuits aimed at high-capacity optical applications. This article is protected by copyright. All rights reserved.

N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document}=4 Supergravity with Local Scaling Symmetry in Four Dimensions

We construct the most general four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 supergravity coupled to an arbitrary number n of vector multiplets in which the global scaling symmetry is gauged, in addition to a subgroup of SL(2, ℝ) × SO(6, n). The various gaugings are parametrized by an embedding tensor built out of 2n+63+4n+6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ 2\\left(\\begin{array}{c}n+6\\\\ {}3\\end{array}\\right)+4\\left(n+6\\right) $$\\end{document} parameters that satisfy a specific set of quadratic consistency constraints, to which we provide explicit solutions. We also derive the local supersymmetry transformation rules and the equations of motion for the four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 matter-coupled supergravity with local scaling symmetry. Such supergravity theories do not possess an action, since the scaling symmetry is only an on-shell symmetry of the corresponding ungauged theories.

Insight of hydrogen evolution reaction in slab SnO2 loaded with transition metal atoms

Abstract The utilization of hydrogen energy has emerged as a promising solution for clean and sustainable energy sources. The development of cost-effective catalysts with high activity and stability is crucial for efficient hydrogen production. In this work, we investigated the hydrogen evolution reaction catalytic activity of single transition metal atom (TM = V, Cr, Mn, Fe, Co, Ni) on slab SnO2 by using density functional theory. Our results revealed that the catalytic activity of the slab SnO2 can be significantly enhanced by loading the transition atom. By calculating the Gibbs free energies and exchange current densities in different adsorption configurations of TM-SnO2, single-atom catalyst of Mn-loaded single-atom catalyst exhibits excellent catalytic performance, characterized by a low Gibbs free energy barrier (-0.05 eV). Introducing a transition metal on the SnO2 surface breaks its local symmetry, while the strong coupling between the metal and H atoms enhances catalytic performance. The synergetic effect of symmetry breaking and metal-H interaction boosts overall catalytic activity. This work not only proposes a novel non-platinum HER catalyst based on SnO2 but also lays a solid foundation for future applications of SnO2-based catalysts.

Modification of Local Site Preference for Achieving Tunable Color Emission from Blue to Near-White in Sr3(PO4)2:Dy3+ Phosphor

The color tunability of Sr3(PO4)2:1%Dy3+ phosphor from blue to near white is studied at various annealing conditions. Higher temperature annealing promotes agglomerated rhombohedral (α) phase formation. Experimental and theoretical analysis reveal dopant preference at the low-symmetry Sr(II) site, altering electric (4F9/2→6H13/2) and magnetic (4F9/2→6H15/2) dipole transitions, thereby affecting the yellow-to-blue (Y/B) ratio. The luminescence intensity variation and color tunability are explained based on the local site symmetry and occupation probability of the dopant in the host lattice. An increase in the luminescence intensity up to an annealing temperature of 1200°C, followed by quenching is observed due to the oxygen vacancies. Commission Internationale d'Eclairage (CIE) color coordinates of (0.31, 0.38), Correlated Color Temperature (CCT) of 6341 K, and color purity of 22.57% confirm the potential of Sr3(PO4)2:1%Dy3+ phosphor annealed at (1200°C, 6hrs) for white light generation. A probable photoluminescence mechanism involving 4f→5d→4f transitions in Sr3(PO4)2:1%Dy3+ is proposed.

Local disorder of multi-site of Eu dopant and its effect on spectroscopy properties in NaCaPO4 host

Optical spectroscopy and defect disorder of multi-site of Eu dopant in NaCaPO4 structure was studied by computational and experimental methods. The prediction of intrinsic disorder and the symmetry and detailed geometry of multi-site of Eu dopant was made by atomistic modeling. The crystal field parameters are then calculated and used to obtain the 7F1 sublevels of the Eu3+ ion, which we used to discuss the local symmetry of the multi-site of Eu3+. The calculations suggest that the most energetically feasible configurations involve the substitution of Eu3+ and Eu2+ ions at the Ca2 site. For Eu3+ substitution, charge charge compensation by defect is the most provable. The solution energies for the other configuration, for the two Eu3+ dopant ions, are very similar. This means that the Eu3+ dopant can be found in all Ca sites in the NaCaPO4. The theoretical spectroscopic study showed that the symmetry of the Eu3+ ions, based on the amount of non-null crystal field parameters, is a C4 symmetry for all multi-site of Eu3+. A set of phenomenological charge factors and the 7F1 manifold split were satisfactorily reproduced in agreement with the experimental data.

Nonequilibrium Criticality at the Onset of Time-Crystalline Order.

We explore the phase transitions at the onset of time-crystalline order in O(N) models driven out of equilibrium. The spontaneous breaking of time translation symmetry and its Goldstone mode are captured by an effective description with O(N)×SO(2) symmetry, where the emergent external SO(2) results from a transmutation of the internal symmetry of time translations. Using the renormalization group and the ε=4-d expansion in a leading two-loop analysis, we identify a new nonequilibrium universality class. Strikingly, it controls the long-distance physics no matter how small the microscopic breaking of equilibrium conditions is. The O(N=2)×SO(2) symmetry group is realized for magnon condensation in pumped yttrium iron garnet films and in exciton-polariton systems with a polarization degree of freedom.

Unraveling volcano trend in OER of metal–organic frameworks with asymmetric configuration through energy band engineering

Local symmetry breaking of catalysts has emerged as an effective strategy for finely tuning oxygen evolution reaction (OER) activity, yet the fundamental comprehension regarding asymmetric structure-activity relationships remains limited. Here, we propose the energy band engineering to bridge the correlation between established asymmetric electronic structure and adsorption/desorption ability of reaction intermediates within metal-organic frameworks (MOFs). The deliberate synthesis of CoM-MOFs (M=Cu, Ni, and Fe) with distinct coordination microenvironments enables the customization of asymmetric Co-O-M electronic structure. A volcano-shaped relationship can be revealed between calculated OER overpotential and average d‐band center (Ed) energy level for both active Co sites and substituted M. The CoFe-MOF, located close to the summit, showcases the balanced reaction intermediate behavior and thus for enhanced OER activity. This work presents a promising approach to thoroughly understand asymmetric electronic structure-activity relationships from the perspective of energy band engineering and further guide the discovery of high-efficiency MOF-based OER catalysts.

Structural, morphological, spectral properties and high quantum efficiency of Eu3+, B3+ co-activated double perovskite Ba2GdMO6 (M = Nb, Ta) phosphors

The influence of boron on the structural, morphological, and spectral properties was examined using Ba2Gd1−xMO6 (M = Nb, Ta) double perovskite ceramics co-doped with xEu3+ and yB3+ (x = 10 mol%, y = 0, 5, 15, 30, 50, 70, 100 mol%), which were synthesized through the solid-state method. X-ray diffractions of all the samples revealed a single-phase structure, and SEM micrographs of B3+, Eu3+ doped grains showed that the flux effect of boron promotes grain growth. The optical band gap energy was calculated from UV–Vis reflectance spectra, where Eg values decreased between 0 and 100 B3+. PL emissions of phosphors increase up to 50 mol% B3+ concentration due to increasing grain size and improving crystallinity, while a somewhat increase occurred in the asymmetry ratio for both series. The increase of the Judd-Ofelt (JO) parameters (Ω2 and Ω4) with increasing B3+ was associated with the decreasing local symmetry of Eu3+ sites and the decreasing electron density in the ligands. Moreover, while the increase of boron improved the quantum efficiency of phosphors, the ηQE% values of 50 mol% B3+ concentration were 80.84 % and 98.02 % for Ba2Gd1-xMO6:xEu3+, yB3+ (M = Nb, Ta), respectively. The paper may provide an alternative perspective and a new strategy for the structural, morphology, and luminescence efficiency of RE3+-doped double perovskite phosphors.

Magnetic coupling interaction-related photoluminescence behaviors in all-inorganic manganese chloride perovskites

Manganese halides, as dilute magnetic semiconductor materials, have magnetic coupling interactions that play an essential role in their photoluminescence (PL); however, such interactions remain controversial. AMnCl3 (AMC, A = K, Rb, and Cs) and their hydrates AMnCl3·2H2O (AMCH, A = K, Rb, and Cs) are both in the ABX3 configuration but exhibit a wide variety of structures with different connectivity types and dimensions. Their magnetic coupling interaction has been demonstrated. However, few studies have systematically investigated the PL in conjunction with the magnetic coupling interaction over these chloride compounds. In this paper, the effect of the magnetic coupling interaction on AMC and AMCH PL is mainly revealed by temperature-dependent PL spectra and lifetimes. The MnX6 (X6 = Cl4(H2O)2 or Cl6) cluster connection types affect the Mn2+–Mn2+ distances. The magnetic coupling interaction between MnX6 octahedrons affects the radiative transitions of manganese chlorides, which is influenced by the Mn2+–Mn2+ distance, local symmetry, and water ligand. The Mn2+–Mn2+ distance and the magnetic coupling interaction also affect their lifetimes. Variations in magnetic coupling interactions can shift emission wavelength, especially dual-emissions and near-infrared (NIR) emission at lower temperatures while A+ = K+. This work helps researchers understand the optical process of Mn2+ ions in different manganese compounds and provides new insights into the design of tailored Mn2+ ion phosphors.

AutoEFT: Automated operator construction for effective field theories

The program AutoEFT is described. It allows one to generate Effective Field Theories (EFTs) from a given set of fields and symmetries. Allowed fields include scalars, spinors, gauge bosons, and gravitons. The symmetries can be local or global Lie groups based on U(1) and SU(N). The mass dimension of the EFT is limited only by the available computing resources. The operators are stored in a compact, human and machine-readable format. Aside from the program itself, we provide input files for EFTs based on the Standard Model and a number of its extensions. These include additional particles and symmetries, EFTs with minimal flavor violation, and gravitons. Program summaryProgram title:AutoEFTCPC Library link to program files:https://doi.org/10.17632/z8xm2hpbsp.1Developer's repository link:https://gitlab.com/auto_eft/autoeftLicensing provisions: MIT licenseProgramming language:PythonNature of problem: The bottom-up construction of an Effective Field Theory (EFT) which describes physics below a certain energy scale Λ requires obtaining a set of operators, composed of fields with mass m≪Λ, that are invariant under certain symmetries. One is primarily interested in complete sets of independent operators, called operator bases. Their construction for a given mass dimension of the operators is nontrivial due to algebraic and kinematic relations that may render different operators redundant. Except for the lowest mass dimensions, the number of operators is so large that the task of constructing an explicit EFT operator basis requires a high degree of automation on a computer. In addition, an automated approach will allow one to immediately take into account newly postulated or discovered light particles beyond the Standard Model.Solution method: Based on the group theoretical techniques and concepts established in Refs. [1–9] and in particular Refs. [10,11], we developed the program AutoEFT, capable of constructing a non-redundant on-shell operator basis for general EFTs and arbitrary mass dimension. Provided a suitable model file, the respective operator basis is generated explicitly, including contractions of the symmetry group indices, in a fully automated fashion. Due to the generality of the algorithm, it can be applied to a variety of low-energy scenarios. The underlying low-energy theory is encoded in a model file which defines the symmetries and the field content. The fairly simple format enables the user to compose their own model files and to construct the respective operator basis with minimal effort.Additional comments including restrictions and unusual features: In its current form, AutoEFT is restricted to theories including particles with spin 0, 1/2, 1, and 2, where the latter two are considered massless. In addition, AutoEFT only constructs operators that mediate proper interactions, meaning that any operator must be composed of at least three fields. The internal symmetries must be given as factors of U(1) and SU(N) groups. In principle, operator bases can be generated for any mass dimension, which is, however, limited by the available computing resources.

The rule of four: anomalous distributions in the stoichiometries of inorganic compounds

Why are materials with specific characteristics more abundant than others? This is a fundamental question in materials science and one that is traditionally difficult to tackle, given the vastness of compositional and configurational space. We highlight here the anomalous abundance of inorganic compounds whose primitive unit cell contains a number of atoms that is a multiple of four. This occurrence—named here the rule of four—has to our knowledge not previously been reported or studied. Here, we first highlight the rule’s existence, especially notable when restricting oneself to experimentally known compounds, and explore its possible relationship with established descriptors of crystal structures, from symmetries to energies. We then investigate this relative abundance by looking at structural descriptors, both of global (packing configurations) and local (the smooth overlap of atomic positions) nature. Contrary to intuition, the overabundance does not correlate with low-energy or high-symmetry structures; in fact, structures which obey the rule of four are characterized by low symmetries and loosely packed arrangements maximizing the free volume. We are able to correlate this abundance with local structural symmetries, and visualize the results using a hybrid supervised-unsupervised machine learning method.

Superspin chains solutions from 4D Chern-Simons theory

As a generalisation of the correspondence linking 2D integrable systems with 4D Chern-Simons (CS) gauge theory, superspin chains are realized by means of crossing electric and magnetic super line defects in the 4D CS with super gauge symmetry. The oscillator realization of Lax operators solving the RLL relations of integrability is obtained in the gauge theory by extending the notion of Levi decomposition to Lie superalgebras. Based on particular 3-gradings of Lie superalgebras, we obtain graded oscillator Lax matrices for superspin chains with internal symmetries given by A(m − 1 | n − 1), B(m | n), C(n) and D(m | n).

Symmetries and covering maps for the minimal tension string on AdS3× S3× T4

This paper considers a recently-proposed string theory on AdS3 × S3 × T4 with one unit of NS-NS flux (k = 1). We discuss interpretations of the target space, including connections to twistor geometry and a more conventional spacetime interpretation via the Wakimoto representation. We propose an alternative perspective on the role of the Wakimoto formalism in the k = 1 string, for which no large radius limit is required by the inclusion of extra operator insertions in the path integral. This provides an exact Wakimoto description of the worldsheet CFT. We also discuss an additional local worldsheet symmetry, Q(z), that emerges when k = 1 and show that this symmetry plays an important role in the localisation of the path integral to a sum over covering maps. We demonstrate the emergence of a rigid worldsheet translation symmetry in the radial direction of the AdS3, for which again the presence of Q(z) is crucial. We conjecture that this radial symmetry plays a key role in understanding, in the case of the k = 1 string, the encoding of the bulk physics on the two-dimensional boundary.

Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries

We study ’t Hooft anomalies of global symmetries in 1+1d lattice Hamiltonian systems. We consider anomalies in internal and lattice translation symmetries. We derive a microscopic formula for the “anomaly cocycle” using topological defects implementing twisted boundary conditions. The anomaly takes value in the cohomology group H^3(G,U(1)) × H^2(G,U(1))H3(G,U(1))×H2(G,U(1)). The first factor captures the anomaly in the internal symmetry group G, and the second factor corresponds to a generalized Lieb-Schultz-Mattis anomaly involving G and lattice translation. We present a systematic procedure to gauge internal symmetries (that may not act on-site) on the lattice. We show that the anomaly cocycle is the obstruction to gauging the internal symmetry while preserving the lattice translation symmetry. As an application, we construct anomaly-free chiral lattice gauge theories. We demonstrate a one-to-one correspondence between (locality-preserving) symmetry operators and topological defects, which is essential for the results we prove. We also discuss the generalization to fermionic theories. Finally, we construct non-invertible lattice translation symmetries by gauging internal symmetries with a Lieb-Schultz-Mattis anomaly.

Symmetries and anomalies of Kitaev spin-S models: Identifying symmetry-enforced exotic quantum matter

We analyze the internal symmetries and their anomalies in the Kitaev spin-SS models. Importantly, these models have a lattice version of a \mathbb{Z}_2ℤ2 1-form symmetry, denoted by \mathbb{Z}_2^{[1]}ℤ2[1]. There is also an ordinary 0-form \mathbb{Z}_2^{(x)}×\mathbb{Z}_2^{(y)}×\mathbb{Z}_2^Tℤ2(x)×ℤ2(y)×ℤ2T symmetry, where \mathbb{Z}_2^{(x)}×\mathbb{Z}_2^{(y)}ℤ2(x)×ℤ2(y) are \piπ spin rotations around two orthogonal axes, and \mathbb{Z}_2^Tℤ2T is the time reversal symmetry. The anomalies associated with the full \mathbb{Z}_2^{(x)}×\mathbb{Z}_2^{(y)}×\mathbb{Z}_2^T×\mathbb{Z}_2^{[1]}ℤ2(x)×ℤ2(y)×ℤ2T×ℤ2[1] symmetry are classified by \mathbb{Z}_2^{17}ℤ217. We find that for S∈\mathbb{Z}S∈ℤ the model is anomaly-free, while for S∈\mathbb{Z}+\frac{1}{2}S∈ℤ+12 there is an anomaly purely associated with the 1-form symmetry, but there is no anomaly purely associated with the ordinary symmetry or mixed anomaly between the 0-form and 1-form symmetries. The consequences of these symmetries and anomalies apply to not only the Kitaev spin-SS models, but also any of their perturbed versions, assuming that the perturbations are local and respect the symmetries. If these local perturbations are weak, generically these consequences still apply even if the perturbations break the 1-form symmetry. A notable consequence is that there should generically be a deconfined fermionic excitation carrying no fractional quantum number under the \mathbb{Z}_2^{(x)}×\mathbb{Z}_2^{(y)}×\mathbb{Z}_2^Tℤ2(x)×ℤ2(y)×ℤ2T symmetry if S∈\mathbb{Z}+\frac{1}{2}S∈ℤ+12, which implies symmetry-enforced exotic quantum matter. We also discuss the consequences for S∈\mathbb{Z}S∈ℤ.

AHiLS—An Algorithm for Establishing Hierarchy among Detected Weak Local Reflection Symmetries in Raster Images

A new algorithm is presented for detecting the local weak reflection symmetries in raster images. It uses contours extracted from the segmented image. A convex hull is constructed on the contours, and so-called anchor points are placed on it. The bundles of symmetry line candidates are placed in these points. Each line splits the plane into two open half-planes and arranges the contours into three sets: the first contains the contours pierced by the considered line, while the second and the third include the contours located in one or the other half-plane. The contours are then checked for the reflection symmetry. This means looking for self-symmetries in the first set, and symmetric pairs with one contour in the second set and one contour in the third set. The line which is evaluated as the best symmetry line is selected. After that, the symmetric contours are removed from sets two and three. The remaining contours are then checked again for symmetry. A multi-branch tree representing the hierarchy of the detected local symmetries is the result of the algorithm.

Skyrmion lattice in centrosymmetric magnets with local Dzyaloshinsky–Moriya interaction

It is common for the local inversion symmetry to break in crystals, even though the whole crystal has global inversion symmetry. This local inversion symmetry breaking allows for a local Dzyaloshinsky–Moriya interaction (DMI) in magnetic crystals. Here we show that the local DMI can stabilize a skyrmion as a metastable excitation or as a skyrmion crystal in equilibrium. We consider the crystal structure with layered structure as an example, where local inversion is violated in each layer but a global inversion center exists in the middle of the two layers. These skyrmions come in pairs that are related by inversion symmetry. The two skyrmions with opposite helicity in a pair form a bound state. We study the properties of a skyrmion pair in the ferromagnetic background and determine the equilibrium phase diagram, where a robust lattice of skyrmion pairs is stabilized. Our results point to a new direction to search for the skyrmion lattice in centrosymmetric magnets.

Does the accounting of the local symmetry fragments in quasi-SMILES improve the predictive potential of the QSAR models of toxicity toward tadpoles?

Models of toxicity to tadpoles have been developed as single parameters based on special descriptors which are sums of correlation weights, molecular features, and experimental conditions. This information is presented by quasi-SMILES. Fragments of local symmetry (FLS) are involved in the development of the model and the use of FLS correlation weights improves their predictive potential. In addition, the index of ideality correlation (IIC) and correlation intensity index (CII) are compared. These two potential predictive criteria were tested in models built through Monte Carlo optimization. The CII was more effective than IIC for the models considered here.