# Questions tagged [scaling]

Questions involving the laws which are scale invariant, i.e. that apply to different scales equally. Also laws that involve exponential behavior, expressed in terms of certain magnitudes to the power of certain exponents.

139 questions
Filter by
Sorted by
Tagged with
1 vote
23 views

### Scaling equation for the external field H in an Ising like system [closed]

i want to show that the following relation is true for the external field H, starting from the scaling form of the free energy. It is an Ising like System close to a critical point with $M \geq 0$ and ...
• 43
22 views

### Scaling Magnetic Fields Properties

Do magnetic fields of magnets of different mass differ in scale rationally or do the fields change in size and shape exponentially. In other words, would a microscopic magnet magnetic field look the ...
1 vote
55 views

126 views

### Critical exponents and scaling dimension

It is often stated that the scaling exponents, e.g. $\alpha$ and $\beta$, of the critical 2D Ising model are related to the scaling dimensions $\Delta_{\sigma}$ and $\Delta_{\epsilon}$ of the ...
61 views

### How to Prove A Claim made to Construct the Calabrese-Lefevre Distribution?

My question is a mathematical one based on this physics paper. Suppose that $\lambda_i$ is an eigenvalue of a reduced density matrix. Up to a normalization factor, the distribution of eigenvalues is ...
1 vote
79 views

### When scaling down a universe, what is scaled down, and how to calculate gravity?

Assume I want to scale down Earth so that it fit into a 500x500 units (pixels) cartesian plane, at a scale of 1:1,000,000. Earth, with a radius of 6,371,000 meters, now has a radius of 6.371 units. ...
• 13
83 views

### Scaling of resistance in different dimensions

Reading a pedagogical article by Steve Girvin on the quantum Hall effect, I noticed a result that in principle I have known for a long time, but I had never actually noticed. In $\rm 1D$, resistance ...
• 2,405
366 views

### How can the scaling dimension of a scalar field be $1$ in a $1d$ CFT?

In a one-dimensional scalar field theory, the kinetic term of the action takes the following form: $$S_\text{kin} = \int_\mathbb{R} dt\, \frac{1}{2} \dot{\varphi}(t) \dot{\varphi}(t)\,, \tag{1}$$ with ...
• 1,723
97 views

### What kind of matter's energy density scales as the inverse of the scale factor

We know that radiation energy density scales as $a^{-4}$ with EoS parameter ($w=\frac{1}{3}$), matter as $a^{-3}$ with ($w=0$), curvature as $a^{-2}$ with ($w=-\frac{1}{3}$). Then which kind of matter ...
• 682
444 views

### In terms of compressive stress $F/A$, what is the cross-sectional area of a sphere?

Any physics textbook chapter on stress-strain curves will generally mention that stress is force acting upon an area, and when a shape is three-dimensional, that area is the cross-sectional area. ...
• 23
66 views

### Test tank physics

In a test tank scaled-down simulation of, for example, a ship stability problem, is it not incorrect to assume that water will behave in a scaled-down fashion with regard to wave period? Don't we need ...
1 vote
126 views

### Mathematical Reasoning In Physics

Does this form of reasoning have a name. I often see it but am a little confused on how to read/understand it and wanted to look more into it but don't know what to call it Ex. Let's call the force ...
• 139
365 views

### How do water waves scale up as the size of a bathtub scales up?

If I fill a bathtub with water to the point that it is spilling out of the far end of the tub, the waves in the tub caused by the water coming into the basin stabilize at a given height -- roughly two ...
• 196
365 views

### Are infinitesimal dilatation transformations local?

In quantum field theories, a local transformation of a scalar field $\phi(x)$ is a transformation that involves the field and its derivatives at same point. See for instance Weinberg's QFT textbok, ...
• 11.9k
142 views

### Scaling dimension/weight of $\partial^{\mu}$

Under a scale transformation $x^{\mu}\rightarrow x^{'\mu}=\lambda x^{\mu}$. The operator $\partial_{\mu}$ has the conformal weight $1$ as $\partial_{\mu}^{'}=\frac{1}{\lambda}\partial_{\mu}$. I'm ...
• 3,043
268 views

### Fisher exponent and fractal structure

In the context of critical phenomena, there are several critical exponents commonly used to characterize the singular behaviour at the point of phase transition. The Fisher exponent $\eta$ is defined ...
• 498
50 views

### What is the meaning of a non-canonical fixed point in the RG flow?

Consider, as an example, the Gaussian model: $$S[\phi]=\int\mathrm{d}\vec x\left[\frac{\gamma}{2}\left(\nabla\phi\right)^2+\frac{\mu^2}{2}\phi^2\right].$$ RG analysis can be performed exactly by ...
1 vote
191 views

### Is this quantum mechanical proof of the virial theorem general?

I have seen the following proof for the virial theorem in QM using the variational method. It goes like this: Suppose an exact eigenstate of the system is $\psi(\vec{r})$ and consider a variational ...
• 2,604
79 views

### Equations homogeneous in $X$ and $y$

Arfken and Weber in their mathematical methods for physicists edition 6 on page 334 talk about equations homogeneous in $X$ and $y$ and tells they are homogeneous if the combined powers of $X$ and $y$ ...
33 views

### How can one compute an effective probability at the critical point of a first order phase transition

In an excerpt from Finite-Size Scaling by John Cardy I found the following development: At a first-order transition, the correlation length ξ remains finite, and the finite-size scaling properties in ...
• 127
134 views

### Scaling limit, renormalization group and low-energy effective field theories

Given a quantum lattice theory $T_0$, e.g., in one dimension defined on $L$ sites, I know that there is a scaling limit, which introduces a lattice scale $a_0$ and keeps the following two quantities ...
• 813
1 vote
73 views

• 1,200
6k views

Why do objects with big size break easily? For example: if I drop a chalk of length $L$ from height $h$ then there is a greater probability that it might break, when compared it to a chalk of length $\... • 1,691 6 votes 1 answer 229 views ### One-point function in CFT on an infinite strip through scaling analysis In Philippe Di Francesco's book on Conformal Field Theory in section 11.2.3 on the Infinite Strip, the one point function of a primary operator (with scaling dimension$\Delta$) is calculated by ... • 372 3 votes 1 answer 212 views ### Does the action remain dimensionless after the renormalization? After the renormalization procedure, fields will gain an anomalous dimension,$\gamma$, which means that their scaling dimension will be different from what we would guess from the dimensional ... 4 votes 1 answer 261 views ### Picture of poor man's scaling for AFM/FM interaction in Kondo problem Poor man's scaling in Kondo problem For the Kondo model: $$H=-t\sum_{i,j}c_i^\dagger c_j+JS\cdot \sigma(0)$$ which only including itinerant electrons with the band-width$ W \in[-D,D]$, and$S$is the ... • 1,602 1 vote 2 answers 130 views ### Explain how scaling of the inverse square law breaks down at a stars surface If the radiation pressure at distance$d>R$from the center of an isotropic black body star is found to be$\$P_{rad}=\large{\frac{4\sigma T^4}{3c}}\left[1-\left(1-\frac{R^2}{d^2}\right)^{\frac{3}{2}...
• 11
Consider a field theory, and a rescaling transformation of the coordinates $$T_\epsilon[\phi(x)]=\phi((1+\epsilon)x).$$ From what I understand, one usually requires that, ...