Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Ferromagnetism

Ferromagnetism

Materials like iron, nickel, and cobalt consist of magnetic domains, within which the magnetic dipoles are arranged parallel to each other. The magnetic dipoles are rigidly aligned in the same direction within a domain by quantum mechanical coupling among the atoms. This coupling is so strong that even thermal agitation at room temperature cannot break it. The result is that each domain has a net dipole moment. However, some materials have weaker coupling, and are ferromagnetic at lower...

Atomic Nuclei: Nuclear Relaxation Processes

Atomic Nuclei: Nuclear Relaxation Processes

In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis, the precessing magnetic moments are randomly oriented around the z-axis. This...

Atomic Nuclei: Nuclear Spin State Overview

Atomic Nuclei: Nuclear Spin State Overview

NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...

Diamagnetism

Diamagnetism

Materials consisting of paired electrons have zero net magnetic moments. However, when these materials are placed under an external magnetic field, the moments opposite to the field are induced. Such materials are called diamagnets. Diamagnetism is the response of the diamagnets when placed in an external magnetic field.
Diamagnetism was discovered by Anton Brugmans in 1778 when he observed that bismuth gets repelled by magnetic fields, thus theorizing that diamagnets get repelled by magnets.

Valence Bond Theory

Valence Bond Theory

Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...

Paramagnetism

Paramagnetism

Paramagnets are materials with unpaired electrons that possess a finite magnetic moment. In the absence of a magnetic field, these moments are randomly oriented, and thus the net moment is zero. Under an external field, a torque acting on the moments tends to align them along the field's direction. However, the random thermal motion of electrons produces a torque opposite to the external field and tries to disorient the moments. These two competing effects align only a few moments along the...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Approximate master equations for the spatial public goods game.

Physical review. E·2024

Same author

Synergistic epidemic spreading in correlated networks.

Physical review. E·2022

Same author

Improving thermal and mechanical properties of biomass-based polymers using structurally ordered polyesters from ricinoleic acid and 4-hydroxycinnamic acids.

RSC advances·2022

Same author

Structure of percolating clusters in random clustered networks.

Physical review. E·2020

Same author

Efficiency of prompt quarantine measures on a susceptible-infected-removed model in networks.

Physical review. E·2017

Same author

Outbreaks in susceptible-infected-removed epidemics with multiple seeds.

Physical review. E·2016

Search research articles

Related Experiment Video

Updated: Jun 19, 2026

Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains

Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains

Published on: July 20, 2022

Ferromagnetic Ising spin systems on the growing random tree.

Takehisa Hasegawa¹, Koji Nemoto

¹Department of Physics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido 060-0810, Japan. hase@statphys.sci.hokudai.ac.jp

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 2, 2009

Summary

This summary is machine-generated.

We analyzed the ferromagnetic Ising model on scale-free trees. Our findings estimate the divergent temperature (T(s)) related to the attachment parameter (alpha) and ferromagnetic interaction (J).

More Related Videos

Visualizing Uniaxial-strain Manipulation of Antiferromagnetic Domains in Fe1+YTe Using a Spin-polarized Scanning Tunneling Microscope

Visualizing Uniaxial-strain Manipulation of Antiferromagnetic Domains in Fe₁₊_YTe Using a Spin-polarized Scanning Tunneling Microscope

Published on: March 24, 2019

Sputter Growth and Characterization of Metamagnetic B2-ordered FeRh Epilayers

Sputter Growth and Characterization of Metamagnetic B2-ordered FeRh Epilayers

Published on: October 5, 2013

Related Experiment Videos

Last Updated: Jun 19, 2026

Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains

Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains

Published on: July 20, 2022

Visualizing Uniaxial-strain Manipulation of Antiferromagnetic Domains in Fe1+YTe Using a Spin-polarized Scanning Tunneling Microscope

Visualizing Uniaxial-strain Manipulation of Antiferromagnetic Domains in Fe₁₊_YTe Using a Spin-polarized Scanning Tunneling Microscope

Published on: March 24, 2019

Sputter Growth and Characterization of Metamagnetic B2-ordered FeRh Epilayers

Sputter Growth and Characterization of Metamagnetic B2-ordered FeRh Epilayers

Published on: October 5, 2013

Area of Science:

Statistical Mechanics
Complex Systems
Network Theory

Background:

The ferromagnetic Ising model is a fundamental model in statistical mechanics.
Scale-free networks exhibit unique topological properties influencing system behavior.
Understanding phase transitions in complex network structures is crucial.

Purpose of the Study:

To analyze the ferromagnetic Ising model on a specific scale-free tree: the growing random tree model.
To derive an estimate for the divergent temperature (T(s)) where zero-field susceptibility diverges.
To investigate the relationship between T(s), the attachment parameter (alpha), and ferromagnetic interaction (J).

Main Methods:

Utilizing the growing random tree model with a linear attachment kernel (A(k) = k + alpha).
Deriving a theoretical estimate for the divergent temperature T(s).
Performing analysis of an exactly solvable limit and numerical calculations for validation.

Main Results:

An explicit relationship between the divergent temperature T(s) and the parameter alpha was derived: tanh(J/T(s)) = alpha/[2(alpha+1)].
The derived estimate for T(s) shows a clear dependence on the network's growth parameter alpha.
The study provides a quantitative link between network topology and magnetic properties.

Conclusions:

The derived formula provides a reliable estimate for the divergent temperature in this scale-free ferromagnetic Ising model.
Both analytical solutions in specific limits and numerical computations confirm the validity of the findings.
This research contributes to understanding critical phenomena in complex network systems.