Related Experiment Video
Updated: Aug 6, 2026
11:19
Site Directed Spin Labeling and EPR Spectroscopic Studies of Pentameric Ligand-Gated Ion Channels
Published on: July 4, 2016
Relationship between Heider links and Ising spins
Zdzislaw Burda1, Maciej Wołoszyn1, Krzysztof Malarz1
1AGH University, Faculty of Physics and Applied Computer Science, al. Mickiewicza 30, 30-059 Kraków, Poland.
Physical Review. E
|July 24, 2026
Summary
The Heider model, when structurally balanced, mirrors the Ising model. This equivalence reveals that balanced social states exhibit a phase transition, similar to magnetic systems.
Area of Science:
- Social psychology
- Statistical mechanics
- Network theory
Background:
- The Heider model describes social balance in triadic relationships.
- The Ising model is a fundamental tool in statistical mechanics for understanding magnetism.
Purpose of the Study:
- To establish a formal equivalence between the Heider model and the Ising model.
- To explore the implications of this equivalence for understanding social phase transitions.
Main Methods:
- Mathematical modeling of social interactions.
- Graph theory to represent social networks.
- Analysis of structural balance conditions.
Main Results:
- Demonstrated equivalence between the Heider model (with external field) and the Ising model (nearest-neighbor interactions) in the limit of structural balance.
- Represented signs of Heider relations as Ising spin products.
- Showcased explicit proof for complete graphs and a general argument for arbitrary graphs.
Conclusions:
- The Heider model's balanced states exhibit a phase transition, analogous to the Ising model.
- This transition occurs at a critical social field value where edge magnetization fluctuations are maximized.
Related Concept Videos
01:22Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)
Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...
01:20Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)
Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
01:17Spin–Spin Coupling: One-Bond Coupling
Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
01:08Spin–Spin Coupling Constant: Overview
In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...
03:06The Pauli Exclusion Principle
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
01:08NMR Spectroscopy: Spin–Spin Coupling
The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved in...