Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

On some modified spherical models.

W W Barrett1, M Kac

  • 1Department of Mathematics, University of Wisconsin, Madison, Wisc. 53706.

Proceedings of the National Academy of Sciences of the United States of America
|December 1, 1975
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

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

Sort by
Same author

Solid-phase microextraction of hop volatiles. Potential use for determination and verification of hop varieties.

Journal of chromatography. A·2001
Same author

Severe injuries in children related to improvised sledging.

Acta paediatrica (Oslo, Norway : 1992)·2000
Same author

Update in the treatment of schizophrenia.

Australian family physician·1993
Same author

Yosif begun.

Science (New York, N.Y.)·1984
Same author

Marginalia. Statistical odds and ends.

American scientist·1983
Same author

Degrees revoked in soviet union.

Science (New York, N.Y.)·1982
Same journal

Chemotactic self-organization captures the dynamics of mammalian hair follicle patterning.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Tomographic imaging of superconducting order using particle-hole interference.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Inhibitory potential of autologous neutralizing antibodies sets quantitative limits on the rebound-competent HIV-1 reservoir.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Inferring epidemiological parameters under an infectious phylogeography model with visitor dynamics.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Analytical modeling for suction cup designs for skin-interfaced wearable devices.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Improving cell-free metabolism through direct integration of artificial respiratory chains.

Proceedings of the National Academy of Sciences of the United States of America·2026
See all related articles

This study introduces a new family of models related to the spherical model. For positive parameter values, these models exhibit Ising-like symmetry and are conjectured to share the same phase transition critical temperature.

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • The spherical model is a fundamental model in statistical mechanics.
  • Understanding phase transitions is crucial for various physical systems.

Purpose of the Study:

  • To investigate a one-parameter family of models generalizing the spherical model.
  • To explore the phase transition behavior of these generalized models.

Main Methods:

  • Consideration of a one-parameter family of models, where alpha=0 corresponds to the spherical model.
  • Heuristic discussion of phase transitions and symmetry properties (close to Ising model for alpha > 0).
  • Checking the conjecture on a mean-field model.

Main Results:

  • Models with alpha > 0 display symmetry akin to the Ising model.

Related Experiment Videos

  • A conjecture is proposed: if the spherical model (alpha=0) has a phase transition, so do models with alpha > 0.
  • The critical temperature is conjectured to remain the same for small alpha > 0.

    • Conclusions:

    • The generalized models offer insights into phase transitions beyond the standard spherical model.
    • The conjecture suggests a robust nature of phase transitions under small perturbations.
    • Mean-field analysis supports the conjecture regarding critical temperature preservation.