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Related Concept Videos

Electrostatic Boundary Conditions01:16

Electrostatic Boundary Conditions

Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
Continuous Charge Distributions01:17

Continuous Charge Distributions

Imagine a bucket of water. It contains many molecules, of the order of 1026 molecules. Thus, although it contains discrete elements (molecules) at the microscopic level, macroscopically, it can be considered continuous. Small volume elements of water, infinitesimal compared to the bulk of the bucket's volume, still contain many molecules. Under this framework, quantized matter is approximated as continuous for practical purposes.
The electric charge can also be subjected to an analogical...
Probability Distributions01:32

Probability Distributions

The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability...
Applications of Integration to Probability Density Functions01:27

Applications of Integration to Probability Density Functions

Continuous probability distributions are used to model random variables that can take on any real value within a specified range. These variables do not take on isolated or countable values but rather exist on a continuum. For example, the height of an individual can be measured with increasing precision—such as 163.5 or 165.25 centimeters—demonstrating that height is a continuous random variable.The behavior of such variables is described using a probability density function (PDF), which...
Magnetostatic Boundary Conditions01:28

Magnetostatic Boundary Conditions

An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
Random Variables01:09

Random Variables

A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...

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Related Experiment Video

Updated: May 30, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Multicritical behavior in a random-field Ising model under a continuous-field probability distribution.

Octavio R Salmon1, Nuno Crokidakis, Fernando D Nobre

  • 1Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro-RJ, Brazil.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|August 6, 2011
PubMed
Summary
This summary is machine-generated.

This study explores a random-field Ising model with a triple Gaussian magnetic field, revealing complex multicritical phenomena and phase diagrams. Increasing randomness can smear out these critical behaviors, mirroring real-world systems.

Related Experiment Videos

Last Updated: May 30, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Investigating multicritical phenomena in magnetic systems is crucial for understanding phase transitions.
  • Random magnetic fields introduce complexity and can alter critical behavior.

Purpose of the Study:

  • To investigate a random-field Ising model with a triple Gaussian magnetic field.
  • To explore the rich variety of multicritical phenomena and phase diagrams.
  • To understand the effect of increasing randomness on these phenomena.

Main Methods:

  • Utilizing the replica method for theoretical analysis.
  • Obtaining phase diagrams within the stable replica-symmetric solution.

Main Results:

  • The model exhibits diverse phase diagrams with multiple ferromagnetic phases and various transition lines (continuous, first-order).
  • Complex multicritical points, including tricritical and fourth-order points, are observed.
  • Increased randomness (larger σ) can lead to the smearing of multicritical phenomena.

Conclusions:

  • The triple Gaussian random-field Ising model provides a versatile framework for studying complex phase transitions.
  • The model's behavior, particularly the smearing of critical phenomena with increased randomness, is relevant to physical systems like diluted antiferromagnets.
  • The findings offer insights into the intricate interplay between interactions, randomness, and phase behavior in magnetic materials.