# Tag Info

### Why does the Earth even have a magnetic field?

The crucial part is that earth's outer core is fluid, and that it's conductive. That the material happens to be iron which we know as ferromagnetic is actually rather unimportant, because the ...
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### Why does the Earth even have a magnetic field?

The core of the Earth isn't a giant bar magnet in the sense that the underlying principles are different. A bar magnet gets its magnetic field from ferromagnetism while Earth's magnetic field is due ...

### Would a compass with unmagnetized needle work?

For an unmagnetized iron needle to align with an external magnetic field, the field would need to be able to induce a magnetization in the needle. This is definitely possible with a large enough field....
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### Why do little chips break off so easily from strong neodymium magnets?

The Neodymium magnets that you use are not actually made from solid chunks of metal, but are rather made by compressing a large amount of powder into blocks through a process called sintering. This is ...
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### What is so special about spontaneous symmetry breaking? (time reversal example)

Indeed, one of the definitions of spontaneous symmetry breaking is in terms of its susceptibility: Suppose we add a symmetry breaking perturbation $h \; \delta H$ to our Hamiltonian (as you do), ...
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### Area in hysteresis loop = energy lost?

Consider the simple ferromagnetic system shown below. The instantaneous power consumed by the system at any time $t$ is simply: $$p(t) = v(t)i(t)$$ Where $v(t)$ and $i(t)$ are simply the voltage and ...
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### Why Curie temperature is bigger for smaller lattice in 2D Ising model

Why numerical simulation gives seemingly wrong result? The exact expression for $T_c$ is given by $$T_c=\frac{2J}{\ln\left(\sqrt{2}+1\right)}\approx 2.269\,J,$$ where we assume that $k_B=1$. This ...
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### Microcanonical ensemble, ergodicity and symmetry breaking

First, I strongly advise you to read sections 24 and 25 of Tolman's excellent book on statistical mechanics. My answer will mainly go along the lines of what is in the book. The ergodic hypothesis ...
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### Would a compass with unmagnetized needle work?

A magnetic dipole would be induced in the iron bar and the iron bar would try and align itself along the magnetic field lines because of the torque applied on it by the interaction of the induced ...
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### I've read that spontaneous symmetry breaking is similar to what happens in ferromagnetism, but are they similar mathematically?

Spontaneous symmetry breaking isn't defined to refer only to what the Higgs field does; it's a much more general phenomenon, of which ferromagnetism is an example. In fact, both examples result from ...
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### Metals and Magnets

Newton's Third Law tells us that if object A exerts a force on object B then object B will exert an equal and opposite force on object A (this is required by the principle of conservation of momentum)....
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### Free energy functions are analytic or non-analytic in phase transitions?

Landau free energy is just an approximation to the real free energy in the thermodynamic limit. For that reason, Landau free energy can be analytic, while the real one is not. Let me show how the ...
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### Why do spinning electrons generate magnetic dipole moments?

Currently our best model of the electron is that it is a point particle. Measurements give an upper bound of $10^{-22}$ meters on its radius. A point particle has no radius, and thus cannot rotate. ...
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### Why do little chips break off so easily from strong neodymium magnets?

These rare earth magnets are very brittle as you said. From Wikipedia: There are two types: neodymium magnets and samariumâ€“cobalt magnets. Rare-earth magnets are extremely brittle and also vulnerable ...
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### Metals and Magnets

To enlarge slightly upon gandalf61's answer, when a piece of ferromagnetic metal is placed near a magnet, it (temporarily) becomes a magnet too, and so the two magnets then attract each other.
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### Is the boundary between ferromagnetism and paramagnetism well-defined?

It turns out that if you work out the physics behind the magnetism of a material, the magnetisation $M$ obeys a transcendental equation of the form $$M=\tanh\left(\frac{\alpha M+\gamma H}{T}\right)$$ ...
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### Why classical mechanics is not able to explain the net magnetization in ferromagnets?

Often, a statement like in the question is linked to the Bohr-van Leeuwen theorem. However, such a theorem does not say that classical electromagnetism can't explain any form of magnetism in materials....
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### Low temperature behavior for ferromagnets: theoretical and experimental discrepancies

Start from the definition of $\tanh x$ in terms of exponentials \begin{align} \tanh x &= \frac{e^x -e^{-x}}{e^x +e^{-x}}\\ &= \frac{1 - e^{-2x}}{1 + e^{-2x}}\\ &=(1 - e^{-2x})\left(1 - e^{-...
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### Free energy functions are analytic or non-analytic in phase transitions?

The Wikipedia page is being sloppy. They mean that the free energy density is an analytic function of the mean-field order parameter, whereas at a thermal phase transition the free energy density is ...
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### Does a crystalline ferromagnetic solid break the rotational symmetry twice?

It seems like you are confusing spatial rotation symmetry and spin rotation symmetry. They are different symmetries (and both are present in nature). In terms of group theory we will say that spin ...
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### Why are there gaps between two lines of iron filings in a magnetic field?

The magnetic field originating from a bar magnet is continuously decreasing when moving away from the bar magnet. It does not have "lines" of stronger field strength. The lines that are ...
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### What does the $B$-field refer to?

$B$ is the magnetic field. In the Lorentz force law $\vec{F}=q(\vec{E} + \vec{v}\times \vec{B})$, which tells you how charges respond to electric and magnetic fields, the field that appears is $B$, ...
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### Low temperature behavior for ferromagnets: theoretical and experimental discrepancies

For the first question you can rewrite $\tanh$ in terms of exponentials, see e.g. this Math.SE post for details. For the second question, yes, $M(0)$ is the magnetization in the zero temperature limit,...
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### What is the difference between paramagnetic and ferromagnetic?

The definitions of the two kinds of material is the following: A paramagnetic material (in short paramagnet) is not magnetized when there is no external field. However, when put in an external field ...
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### Are there any "induced" forces which are repulsive in nature?

Yes, diamagnetic materials are repelled from the source of magnetic field (pushed in direction of field decrease). For example, bismuth, copper and even water at normal temperatures are diamagnets (...
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### Free energy functions are analytic or non-analytic in phase transitions?

I'll provide one possible answer to your question. I use the language of the Ising ferromagnet/paramagnet phase transition, but this is just for convenience as the same holds much more generally. ...
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### Why does dipole-dipole interaction not lead to ferromagnetic ordering?

The magnetic dipole dipole interaction is just by far too weak. In Stephen Blundell: "Magnetism in Condensed Matter" this is estimated to be on an energy scale of about $10^{-23}$J which may play a ...
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### What is the reason of hysteresis loss?

Hysteresis is a kind of non-time-reversible transition, so it is associated with entropy (which must, in theory, generate heat). Because magnetic materials have crystal structure, the internal ...
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