Determination of paramagnetic and ferromagnetic phases of an Ising model on a third-order Cayley tree

In this present paper, the recurrence equations of an Ising model with three coupling constants on a third-order Cayley tree are obtained. Paramagnetic and ferromagnetic phases associated with the Ising model are characterized. Types of phases and partition functions corresponding to the model are rigorously studied. Exact solutions of the mentioned model are compared with the numerical results given in Ganikhodjaev et al. [J. Concr. Appl. Math., 2011, 9, No. 1, 26-34].

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Ising model on the Cayley tree of third order with inhomogeneous interactions

10.1063/1.5041657 ◽

2018 ◽

Author(s):

Nasir Ganikhodjaev ◽

Huda Husna Binti Ibrahim

Keyword(s):

Ising Model ◽

Cayley Tree ◽

Third Order

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Direct determination of the third order Fermi coupling constants λ1, λ2, λ3 of CO2 from experimental data

Spectrochimica Acta Part A Molecular Spectroscopy ◽

10.1016/0584-8539(88)80092-8 ◽

1988 ◽

Vol 44 (11) ◽

pp. 1195-1199 ◽

Cited By ~ 1

Author(s):

Leila S. Balloomal ◽

Lobna M. Salah ◽

Gilbert Amat

Keyword(s):

Experimental Data ◽

Direct Determination ◽

Coupling Constants ◽

Third Order ◽

The Third

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$\mathit{Ab\!-\!initio}$ Determination of Magnetic Interface Coupling Constants for Magnetic Multilayers

Journal de Physique I ◽

10.1051/jp1:1997133 ◽

1997 ◽

Vol 7 (11) ◽

pp. 1299-1304 ◽

Cited By ~ 4

Author(s):

P. Weinberger ◽

C. Sommers ◽

U. Pustogowa ◽

L. Szunyogh ◽

B. Újfalussy

Keyword(s):

Ab Initio ◽

Magnetic Multilayers ◽

Coupling Constants ◽

Interface Coupling

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Ground states for the ising model with an external field on the Cayley tree

Uzbek Mathematical Journal ◽

10.29229/uzmj.2018-3-15 ◽

2018 ◽

Vol 2018 (3) ◽

pp. 147-155

Author(s):

M.M. Rakhmatullaev ◽

M.A. Rasulova

Keyword(s):

Ising Model ◽

External Field ◽

Cayley Tree ◽

Ground States

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Gradient-Enhanced Inverse-Detected NMR Techniquesfor Determination of 1H-15N Coupling Constants in 2,2-Dimethylpenta-3,4-dienal Derivatives

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19971747 ◽

1997 ◽

Vol 62 (11) ◽

pp. 1747-1753 ◽

Cited By ~ 5

Author(s):

Radek Marek

Keyword(s):

Double Bond ◽

Chemical Shifts ◽

Multiple Bond ◽

Coupling Constants ◽

Single Quantum ◽

Nmr Techniques ◽

Phase Sensitive ◽

Heteronuclear Coupling

Determination of 15N chemical shifts and heteronuclear coupling constants of substituted 2,2-dimethylpenta-3,4-dienal hydrazones is presented. The chemical shifts were determined by gradient-enhanced inverse-detected NMR techniques and 1H-15N coupling constants were extracted from phase-sensitive gradient-enhanced single-quantum multiple bond correlation experiments. Stereospecific behaviour of the coupling constants 2J(1H,15N) and 1J(1H,13C) has been used to determine the configuration on a C=N double bond. The above-mentioned compounds exist predominantly as E isomers in deuteriochloroform.

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21,22-Disubstituted 18α,19βH-Ursane Derivatives with Oxabicyclooctane System in Ring E

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19930173 ◽

1993 ◽

Vol 58 (1) ◽

pp. 173-190 ◽

Cited By ~ 1

Author(s):

Eva Klinotová ◽

Jiří Klinot ◽

Václav Křeček ◽

Miloš Buděšínský ◽

Bohumil Máca

Keyword(s):

Spectral Data ◽

Spin Systems ◽

Coupling Constants ◽

Complete Analysis ◽

Nmr Spectrum ◽

Proton Proton ◽

H Nmr ◽

Proton Coupling ◽

C Nmr

Reaction of 3β-acetoxy-21,22-dioxo-18α,19βH-ursan-28,20β-olide (IIIa) and 20β,28-epoxy-21,22-dioxo-19α,19βH-ursan-3β-yl acetate (IIIb) with diazomethane afforded derivatives XII-XIV with spiroepoxide group in position 21 or 22, which were further converted into hydroxy derivatives XV and XVII. Ethylene ketals VIII-X were also prepared. In connection with the determination of position and configuration of the functional groups at C(21) and C(22), the 1H and 13C NMR spectral data of the prepared compounds are discussed. Complete analysis of two four-spin systems in the 1H NMR spectrum of bisethylenedioxy derivative Xb led to the proton-proton coupling constants from which the structure with two 1,4-dioxane rings condensed with ring E, and their conformation, was derived.

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Investigation of zirconium nanowire by elastic, thermal and ultrasonic analysis

Zeitschrift für Naturforschung A ◽

10.1515/zna-2020-0167 ◽

2020 ◽

Vol 75 (12) ◽

pp. 1077-1084

Author(s):

Bhawan Jyoti ◽

Shakti Pratap Singh ◽

Mohit Gupta ◽

Sudhanshu Tripathi ◽

Devraj Singh ◽

...

Keyword(s):

Ultrasonic Attenuation ◽

Thermal Relaxation ◽

Coupling Constants ◽

Physical Parameters ◽

Third Order ◽

Jones Potential ◽

Acoustic Coupling ◽

Anisotropic Factor ◽

Third Order Elastic Constants ◽

Ultrasonic Analysis

AbstractThe elastic, thermal and ultrasonic properties of zirconium nanowire (Zr-NW) have been investigated at room temperature. The second and third order elastic constants (SOECs and TOECs) of Zr-NW have been figured out using the Lennard–Jones Potential model. SOECs have been used to find out the Young’s modulus, bulk modulus, shear modulus, Poisson’s ratio, Pugh’s ratio, Zener anisotropic factor and ultrasonic velocities. Further these associated parameters of Zr-NW have been utilized for the evaluation of the Grüneisen parameters, thermal conductivity, thermal relaxation time, acoustic coupling constants and ultrasonic attenuation. On the basis of the above analyzed properties of Zr-NW, some characteristics features of the chosen nanowire connected with ultrasonic and thermo-physical parameters have been discussed.

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Lee-Yang zeros of the antiferromagnetic Ising model

Ergodic Theory and Dynamical Systems ◽

10.1017/etds.2021.25 ◽

2021 ◽

pp. 1-35

Author(s):

FERENC BENCS ◽

PJOTR BUYS ◽

LORENZO GUERINI ◽

HAN PETERS

Keyword(s):

Ising Model ◽

Partition Functions ◽

Cayley Trees ◽

Circular Arcs ◽

Precise Characterization ◽

Ferromagnetic Ising Model ◽

Location Of Zeros ◽

Antiferromagnetic Ising Model ◽

Recursively Defined Trees ◽

Degree Bound

Abstract We investigate the location of zeros for the partition function of the anti-ferromagnetic Ising model, focusing on the zeros lying on the unit circle. We give a precise characterization for the class of rooted Cayley trees, showing that the zeros are nowhere dense on the most interesting circular arcs. In contrast, we prove that when considering all graphs with a given degree bound, the zeros are dense in a circular sub-arc, implying that Cayley trees are in this sense not extremal. The proofs rely on describing the rational dynamical systems arising when considering ratios of partition functions on recursively defined trees.

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