Showing papers on "Curie–Weiss law published in 2020"
TL;DR: In this paper, a Curie-Weiss model with two groups with different coupling constants within and between groups was discussed, and a central limit theorem was proved for the high-temperature regime.
Abstract: We discuss a Curie–Weiss model with two groups with different coupling constants within and between groups. For the total magnetisations in each group, we show bivariate laws of large numbers and a central limit theorem which is valid in the high-temperature regime. In the critical regime, the total magnetisation normalised by
$$N^{3/4}$$
converges to a non-trivial distribution which is not Gaussian, just as in the single-group Curie–Weiss model. Finally, we prove a kind of a ‘law of large numbers’ in the low-temperature regime, more precisely we prove that the empirical magnetisation converges in distribution to a mixture of two Dirac measures.
23 citations
02 Jul 2020
TL;DR: In this paper, the authors studied the partition function of zeros for the Curie-Weiss model using a cumulant method and elucidated the Lee-Yang zeros and reported on the critical behavior of the system.
Abstract: The authors study the partition function of zeros for the Curie-Weiss model using a cumulant method. The paper elucidates the the Lee-Yang zeros and report on the critical behavior of the system.
20 citations
TL;DR: In this article, rare-earth doping was used to enhance the coupling coefficient of multiferroic composites of BaTiO3 and CoFe2O4 by increasing the cell volume.
Abstract: The present study attempts to enhance the coupling by rare-earth doping in particulate multiferroic composites of BaTiO3 and CoFe2O4. These composites were prepared by conventional solid-state route with the compositions (1-x) Ba0·99Tb0·02Ti0·99O3 – x Co0·94Tb0·06Fe2O4 (x = 0.02, 0.04 and 0.06). The decrease in cell volume of Co0·94Tb0·06Fe2O4 phase with the increase in Co0·94Tb0·06Fe2O4 phase results in the enhancement of strain, which in turn improves the coupling. The Tb3+ ion doping enhances the dielectric constant of composites and the Curie Weiss Law shows the diffused nature of ferroelectric phase transitions. The unification of two ferroic phases in composites has been confirmed by tracing the P-E and M − H hysteresis loops. The P-E loops are free from leakage currents and M − H loops are well saturated, confirming an ordered domain structure. The terbium doping results in high magnetoelectric coupling coefficients, so making these composites as potential candidates for magnetoelectric devices.
9 citations
TL;DR: In this paper, four new lanthanide(III) coordination polymers were synthesized by using 2,5-dihydroxybenzene-1,4-dicarboxylate (Dhbdc, C8H6O62−) as a ligand and characterized by elemental analysis, infrared spectroscopy, TGA-DSC and single crystal X-ray diffraction studies.
Abstract: Four new lanthanide(III) coordination polymers (1–4) have been synthesized by using 2,5-dihydroxybenzene-1,4-dicarboxylate (Dhbdc, C8H6O62−) as a ligand and characterized by elemental analysis, infrared spectroscopy, TGA-DSC (Thermogravimetric Analysis-Differential Scanning Calorimetry) and single crystal X-ray diffraction studies. The isolated complexes include; [Ce(Dhbdc)(H2O)3Cl]n (1) and [Ln(Dhbdc)1.5(H2O)2]n·3n(C2H6O)·nH2O [Ln = Eu (2), Gd (3) and Tb (4)]. The structural analysis reveals that compound 1 is a two-dimensional polymer in which the cerium atoms are coordinated by six oxygen and two bridging chloride ions adopting a dodecahedral geometry. The compounds 2–4 are isomorphous and their extended structures consist of three-dimensional supramolecular frameworks encapsulating [001] channels occupied by the guest water and ethanol molecules. The metal atoms in 2–4 exhibit a square antiprism geometry. All these compounds have O–H⋯O hydrogen bonds originating from the coordinated water and solvent molecules that help to consolidate the structures. The compounds 1, 3 and 4 were investigated for magnetic properties and they exhibited weak antiferromagnetic coupling interactions between the lanthanides as per the Curie Weiss law. Anisotropic nature of 3 and 4 has been depicted as per magnetization versus field plots. Complex 4 behaves as a soft magnetic material as compared to 3. The luminescence studies indicate that compounds 2, 3 and 4 show ligand-centred fluorescence, which is significantly enhanced in the case of 4.
5 citations
TL;DR: In this article, structural, dielectric, ferroelectric and piezoelectric properties of Gd3+ doped lead-free (K0.5Na 0.5)0.96Li 0.04Gd0.8Ta 0.20)O3 (KNLNT) ceramics were reported.
Abstract: We report the structural, dielectric, ferroelectric and piezoelectric properties of Gd3+ doped lead-free (K0.5Na0.5)0.96Li0.04(Nb0.8Ta0.20)O3 (KNLNT) ceramics. The transition temperature (TT-C and TO-T) shifted towards the lower temperature (281 °C and 110 °C) for (K0.5Na0.5)0.92Li0.04Gd0.04(Nb0.8Ta0.20)O3 (KNLGNT) ceramics. Frequency dispersion of TT-C or TO-T suggests that KNLGNT ceramics exhibit a relaxor behavior supported by the Vogel-Fulcher law and modified Curie Weiss law. Temperature-dependent resistivity analysis shows that the conduction mechanism follows Mott’s variable range hopping with an average hopping length of 7.23 nm, hopping energy 0.46 eV and density of states near the Fermi level [N(EF)] = 129 × 1016 eV−1 cm−3 for KNLGNT ceramics. Reduction in leakage current and enhancement in dielectric (er = 1025, tanδ = 0.061 at 1 MHz), ferroelectric properties (Pr = 23.14 μC/cm2, EC = 8.70 kV/cm at 1 Hz) and piezoelectric properties (kp (53%) and d33 (128 pC/N)) were observed for KNLGNT ceramics, which are promising for high-frequency piezoelectric devices.
4 citations
TL;DR: The existence of the Curie-Weiss magnetic response observed in most transition metals that are Fermi liquids at low temperatures has been an enigma for decades and has not yet been fully explained from microscopic principles as discussed by the authors.
Abstract: The genesis of the Curie-Weiss magnetic response observed in most transition metals that are Fermi liquids at low temperatures has been an enigma for decades and has not yet been fully explained from microscopic principles. We show on the single-impurity Anderson model how the quantum dynamics of strong electron correlations leads to the Curie-Weiss magnetic susceptibility sufficiently above the Kondo temperature. Such behavior has not yet been demonstrated and can be observed only when the bare interaction is substantially screened (renormalized) and a balance between quantum and thermal fluctuations is kept. We set quantitative criteria for the existence of the Curie-Weiss law.
3 citations
TL;DR: In this article, a single-sort continuum Curie-Weiss system of interacting particles is studied, where the particles are placed in the space of congruent cubic cells, and each two particles contained in the same cell are subjected to binary repulsion with intensity (J_2>J_1).
Abstract: A single-sort continuum Curie-Weiss system of interacting particles is studied. The particles are placed in the space $\\mathbb{R}^d$ divided into congruent cubic cells. For a region $V\\subset \\mathbb{R}^d$ consisting of $N\\in \\mathbb{N}$ cells, every two particles contained in $V$ attract each other with intensity $J_1/N$. The particles contained in the same cell are subjected to binary repulsion with intensity $J_2>J_1$. For fixed values of the temperature, the interaction intensities, and the chemical potential the thermodynamic phase is defined as a probability measure on the space of occupation numbers of cells, determined by a condition typical of Curie-Weiss theories. It is proved that the half-plane $J_1\\,\\times\\,$\\textit{chemical potential} contains phase coexistence points at which there exist two thermodynamic phases of the system. An equation of state for this system is obtained.