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# Questions tagged [scale-invariance]

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### Conformal transformation/ Weyl scaling are they two different things? Confused!

I see that the weyl transformation is $g_{ab} \to \Omega(x)g_{ab}$ under which Ricci scalar is not invariant. I am a bit puzzled when conformal transformation is defined as those coordinate ...
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### What is the difference between scale invariance and self-similarity?

I always thought that these two terms are some kind of synonyms, meaning that if you have a self-similar or scale invariant system, you can zoom in or out as you like and you will always see the same ...
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### Is $\phi^4$ theory in 4d conformally invariant at the classial level?

I used to believe the three following statements to be true (at the classical level only): From scale invariance full conformal invariance follows. Scale invariance is present if there are no ...
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### What does scale invariance or non-invariance of electromagnetism physically imply?

According to Wikipedia, classical electromagnetism is scale-invariant. I understand what it means mathematically as explained in Wikipedia. But what does it really imply physically? Next, here it ...
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### How to determine correlation length when the correlation function decays as a power law?

I am studying a system for which I observe a power-law decay in the correlation function: $\left\langle s\!\left(0\right)\cdot s\!\left(r\right) \right\rangle \propto r^{-\alpha}$ I am interested in ...
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### Relation of conformal symmetry and traceless energy momentum tensor

In usual string theory, or conformal field theory textbook, they states traceless energy momentum tensor $T_{a}^{\phantom{a}a}=0$ implies (Here energy momentum tensor is usual one which is symmetric ...
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### CFT conformal weight vs. scaling dimension

I was wondering if anybody could clarify what the difference between the conformal scaling dimension $\Delta$ and the conformal weight $h$ is? Is it correctly understood that $\Delta$ is related to ...
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### Do all classical-statistical critical lattice models have emergent conformal invariance?

I understand that any quantum lattice model at the critical point which can be described by a massless relativistic quantum field theory has emergent conformal invariance. My question is what about ...
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### Scale invariance at phase transitions

The Wikipedia entry for scale invariance states In statistical mechanics, scale invariance is a feature of phase transitions. The key observation is that near a phase transition or critical ...
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### How is scale invariance broken in QCD?

It is generally believed that for the pure QCD, the classical scale invariance is broken at the quantum level (therefore anomaly rather than SSB). This breaking of scale invariance may be used to ...
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### Scale relativity vs. scale invariance

What is the difference between Nottale's "scale relativity", and the ordinary concept of scale invariance e.g. that appears in conformal field theory?
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### Why does renormalizability mean that "ultimately locality will have to be abandoned"?

This is stated by Zinn-Justin in his paper Quantum Field Theory: renormalization and the renormalization group: Low energy physics does not depend on all the details of the microscopic model ...
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### Conformally invariant theory. Relationship between conformal transformations and conformal rescaling (Weyl scaling)

So, I'm learning about Twistors, and in every book I've read they say the same: "If a flat theory is Poincaré-invariant and it is invariant under conformal rescaling (Weyl scaling), it is then ...
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### What are marginal fields in CFT?

In this article they call weight $(h,\bar{h})=(1,1)$ fields marginal. Why are these fields called marginal? Why are they to be distinguished.
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### Universality classes

I would like to ask about the universality classes. I know that these are the statistical models which describes different phase transitions with different critical exponents. But I would like to know ...
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### Most general Lagrangian in CFT in 0+1D

My question is about $CFT_1$. Page 18 of this says that $$L={\frac{\overset{.}{Q}^2}{2} - \frac{g}{2Q^2}}\tag{1.11}$$ is the most general Lagrangian that preserves time translation and scale ...
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### Is the Landau free energy scale-invariant at the critical point?

My question is different but based on the same quote from Wikipedia as here. According to Wikipedia, In statistical mechanics, scale invariance is a feature of phase transitions. The key ...
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### RG flow from a UV scale invariant field theory to a gapped phase in the IR

On the section 3 of http://arxiv.org/abs/1309.2921 the authors consider the RG flow from a scale invariant field theory in the UV to a gapped theory in the IR. The theory is couple to a background ...
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### What determines the magnitude of the atmospheric scale height of a planet?

What determines the magnitude of the atmospheric scale height of a planet? https://en.wikipedia.org/wiki/Scale_height says that: "Approximate atmospheric scale heights for selected Solar System ...
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### Is scale invariance an axiom in physics?

Is scale invariance axiomatic within physics, and if so, how does it get around the transition from the microscopic, quantum world, to the macroscopic, classical world?
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### Intuition behind power-law scale invariance

I have seen this notion of a scale-invariant power law curve exhibiting the property that $f(cx) = a(cx)^{-k} = c^{-k}f(x)$, and I am confused about how I should be thinking of this as "scale-...
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### Ising model rescaling

Consider the 2D classical Ising model. It's understood that there is a critical temperature $T_c$, and that the correlation length $\xi(T)$ defined by: \langle \sigma_i \sigma_j \rangle_\mathrm{...
In the case of QCD, the $\Lambda_{QCD}$ introduces a scale in the theory that can be also modified in presence of strongly interacting fermions. This mass-scale breaks the classical scale invariance ...