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

Second Uniqueness Theorem

Second Uniqueness Theorem

Consider a region consisting of several individual conductors with a definite charge density in the region between these conductors. The second uniqueness theorem states that if the total charge on each conductor and the charge density in the in-between region are known, then the electric field can be uniquely determined.
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the surface...

Fundamental Theorem of Algebra

Fundamental Theorem of Algebra

The Fundamental Theorem of Algebra is central to the study of polynomial equations, asserting that every non-constant polynomial with complex coefficients has at least one complex zero. This means that a polynomial of degree n ≥ 1, written as: with an ≠ 0, has at least one solution in the complex number system. Since the set of real numbers is a subset of complex numbers, this theorem applies equally to polynomials with real coefficients.Building on this result, the...

Norton's Theorem

Norton's Theorem

Norton's theorem is a fundamental principle stating that a linear two-terminal circuit can be substituted with an equivalent circuit, which comprises a current source (ⅠN) in parallel with a resistor (RN). Here, ⅠN represents the short-circuit current flowing through the terminals, and RN stands for the input or equivalent resistance at the terminals when all independent sources are deactivated. This implies that the circuit illustrated in Figure (a) can be exchanged with the one...

Castigliano's Theorem

Castigliano's Theorem

Castigliano's theorem analyzes displacements and rotations in elastic structures. It relates the derivative of elastic strain energy to the applied forces or moments, allowing for the calculation of deformations. The theorem states that the partial derivative of the total strain energy of a system with respect to a specific load results in the displacement at the point where the load is applied. This principle applies to both forces and moments.

Thevinin's Theorem

Thevinin's Theorem

Thévenin's theorem plays a pivotal role in electrical circuit analysis, offering a solution to the challenges posed by variable loads within a circuit. In practical applications, it is common to encounter circuits where certain elements remain fixed while others fluctuate, often referred to as the "load." A typical household electrical outlet serves as a prime example of a variable load, as it can be connected to a variety of appliances, each with its own unique electrical characteristics.

Theorems of Pappus and Guldinus

Theorems of Pappus and Guldinus

The two theorems developed by Pappus and Guldinus are widely used in mathematics, engineering, and physics to find the surface area and volume of any body of revolution. This is done by revolving a plane curve around an axis that does not intersect the curve to find its surface area or revolving a plane area around a non-intersecting axis to calculate its volume.
For finding the surface area, consider a differential line element that generates a ring with surface area dA when revolved.

You might also read

Related Articles

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

Sort by

Same author

Fixed-point structure and effective fractional dimensionality for O(N) models with long-range interactions.

Physical review. E, Statistical, nonlinear, and soft matter physics·2015

Same author

Asymptotic freedom in Hořava-Lifshitz gravity.

Physical review letters·2014

Same author

Renormalization group flow of hexatic membranes.

Physical review. E, Statistical, nonlinear, and soft matter physics·2013

Same author

Fixed points of higher-derivative gravity.

Physical review letters·2006

Search research articles

Related Experiment Video

Updated: Apr 25, 2026

Setting Limits on Supersymmetry Using Simplified Models

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

O(N)-universality classes and the Mermin-Wagner theorem.

Alessandro Codello¹, Giulio D'Odorico²

¹SISSA, Via Bonomea 265, 34136 Trieste, Italy.

Physical Review Letters

|August 29, 2014

Summary

This summary is machine-generated.

This study explores how O(N)-symmetric models change with dimension and field components. It reveals new multicritical potentials in fractal dimensions, disappearing at d=2, and an infinite family of O(N=0) universality classes in 2D.

More Related Videos

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

Author Spotlight: Universal Molecular Retention with 11-Fold Expansion Microscopy

Author Spotlight: Universal Molecular Retention with 11-Fold Expansion Microscopy

Published on: October 6, 2023

Related Experiment Videos

Last Updated: Apr 25, 2026

Setting Limits on Supersymmetry Using Simplified Models

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

Author Spotlight: Universal Molecular Retention with 11-Fold Expansion Microscopy

Author Spotlight: Universal Molecular Retention with 11-Fold Expansion Microscopy

Published on: October 6, 2023

Area of Science:

Condensed matter physics
Quantum field theory
Statistical mechanics

Background:

Universality classes describe systems with similar critical behavior.
The Mermin-Wagner-Hohenberg theorem states no spontaneous symmetry breaking in 2D for O(N)-symmetric systems with N>=1.
Renormalization group (RG) methods are crucial for understanding critical phenomena.

Purpose of the Study:

To investigate the continuous dependence of O(N)-symmetric model universality classes on dimension (d) and field components (N).
To understand the emergence of Mermin-Wagner-Hohenberg theorem implications as d approaches 2.
To explore multicritical behavior and O(N=0) universality classes.

Main Methods:

Renormalization group analysis.
Continuous deformation of theory space.
Investigation of effective potentials.

Main Results:

For fractal dimensions 2 < d < 3 and N ≥ 1, a finite family of multicritical effective potentials was found.
These potentials disappear at d = 2 for N ≥ 1, consistent with the Mermin-Wagner-Hohenberg theorem.
An infinite family of O(N=0) universality classes was identified in two dimensions.

Conclusions:

The study provides a continuous picture of universality classes transitioning towards the 2D limit.
It highlights the critical role of dimension and field components in determining critical behavior.
The findings offer new insights into the nature of phase transitions and universality in various dimensions.