On Ising's model of ferromagnetism

Ising discussed the following model of a ferromagnetic body: Assume N elementary magnets of moment μ to be arranged in a regular lattice; each of them is supposed to have only two possible orientations, which we call positive and negative. Assume further that there is an interaction energy U for each pair of neighbouring magnets of opposite direction. Further, there is an external magnetic field of magnitude H such as to produce an additional energy of − μH (+ μH) for each magnet with positive (negative) direction.

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Spherical tensor approach to multipole expansions. II. Magnetostatic interactions

Canadian Journal of Physics ◽

10.1139/p76-058 ◽

1976 ◽

Vol 54 (5) ◽

pp. 513-518 ◽

Cited By ~ 8

Author(s):

C. G. Gray ◽

P. J. Stiles

Keyword(s):

Magnetic Field ◽

External Magnetic Field ◽

Interaction Energy ◽

Current Distribution ◽

Spherical Harmonic ◽

Magnetostatic Interaction ◽

Multipole Expansions ◽

The Magnetic Field ◽

A Current ◽

Magnetostatic Interactions

The magnetic field due to a given current distribution, the interaction energy of a current distribution with an arbitrary external magnetic field, and the magnetostatic interaction energy between two current distributions are decomposed into multipolar components using spherical harmonic expansions. Diamagnetic interactions and the spin contributions to the multipole expansions are also discussed.

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Influence of magnetic field and Rashba spin–orbit coupling on strong-coupling magnetopolarons in quantum disks

International Journal of Modern Physics B ◽

10.1142/s0217979214501859 ◽

2014 ◽

Vol 28 (27) ◽

pp. 1450185

Author(s):

Wei Xin ◽

Chao Han ◽

Eerdunchaolu

Keyword(s):

Magnetic Field ◽

External Magnetic Field ◽

Interaction Energy ◽

Ground State ◽

State Interaction ◽

Orbit Coupling ◽

Spin Orbit Coupling ◽

Spin Orbit ◽

Phonon Interaction ◽

Rashba Spin

On the basis of Lee–Low–Pines (LLP) unitary transformation, the influence of external magnetic field, Rashba spin–orbit coupling and quantum size effect on the ground-state interaction energy of strong-coupling magnetopolarons in quantum disks (QDs) is studied by using the Tokuda improved linear combine operator method. The results show that the ground-state interaction energy of magnetopolarons consists of four parts: the energy caused by the confinement potential of QDs, interaction energy between the electron and external magnetic field, electron and longitudinal-optical (LO) phonon interaction energy and additional term of Rashba effect originating from phonons. The electron–LO phonon interaction energy Ee- ph and additional term of Rashba effect are always negative; the absolute value |Ee- ph | increases with increasing transverse confinement strength ω0, cyclotron frequency of external magnetic field ωc and electron–LO phonon coupling strength α, but decreases with increasing the thickness of QDs L; the state properties of magnetopolarons are closely linked with the sign of the ground-state interaction energy of magnetopolarons E int and change of E int with ωc, ω0, α and L. In addition, the vibration frequency of magnetopolarons λ increases with increasing ωc, ω0 and α, but decreases with increasing L. For the ground state of magnetopolarons in QDs, the electron–LO phonon interaction plays a significant role, meanwhile, the influence of Rashba spin–orbit coupling effect cannot be ignored.

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Remarks on inverse electrodynamics

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09706-4 ◽

2021 ◽

Vol 81 (10) ◽

Author(s):

Patricio Gaete ◽

José A. Helayël-Neto

Keyword(s):

Magnetic Field ◽

External Magnetic Field ◽

Interaction Energy ◽

Coulomb Potential ◽

Nonlinear Electrodynamics ◽

Gauge Invariant ◽

Dependent Variables ◽

Path Dependent ◽

Formula Type ◽

Bending Of Light

AbstractWe study physical aspects for a new nonlinear electrodynamics (inverse electrodynamics). It is shown that this new electrodynamics displays the vacuum birefringence phenomenon in the presence of external magnetic field, hence we compute the bending of light. Afterwards we compute the lowest-order modification to the interaction energy within the framework of the gauge-invariant but path-dependent variables formalism. Our calculations show that the interaction energy contains a long-range ($${1 \big / {{r^5}}}$$ 1 / r 5 -type) correction to the Coulomb potential.

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Diamagnetic Levitation for Passive Tilt Sensors

MRS Proceedings ◽

10.1557/proc-998-j08-16 ◽

2007 ◽

Vol 998 ◽

Cited By ~ 1

Author(s):

Lihong Jiao ◽

Martin Winistöerfer

Keyword(s):

Magnetic Field ◽

External Magnetic Field ◽

External Field ◽

Opposite Direction ◽

Weak Magnetic Field ◽

Magnetic Force ◽

Diamagnetic Susceptibility ◽

Diamagnetic Levitation ◽

Tilt Sensors ◽

The Magnetic Field

ABSTRACTWhen diamagnetic materials are exposed to an external magnetic field, a weak magnetic field in the opposite direction to the external field is induced and a magnetic force is generated causing diamagnetic materials to be expelled from the external magnetic field. The magnitude of the force increases with increase of the magnitude of diamagnetic susceptibility, χm. In this study, the levitation of graphite in the magnetic field was investigated.

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TYPE II ANYON SUPERCONDUCTIVITY

Modern Physics Letters A ◽

10.1142/s0217732395001575 ◽

1995 ◽

Vol 10 (20) ◽

pp. 1455-1462

Author(s):

JEWAN KIM ◽

JUNGDAE KIM ◽

TAEJIN LEE

Keyword(s):

Magnetic Field ◽

Free Energy ◽

External Magnetic Field ◽

Physical Properties ◽

Interaction Energy ◽

Effective Action ◽

Low Energy ◽

Type Ii ◽

Single Vortex ◽

Chern Simons

Assuming that the superconductivity which is described by the low energy effective action of the anyon system may be type II, we discuss its characteristics. We also study physical properties of the Chern-Simons vortices, which may be formed as the external magnetic field is applied to the system, such as their statistics, the free energy of single vortex and the interaction energy between two vortices.

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