All Questions
Tagged with scaling renormalization
20 questions
1
vote
0
answers
25
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
1
vote
0
answers
58
views
Using the RG equations to find the free energy scaling form of the 2D Ising Model
i am trying to calculate the scaling form of the free energy of the 2D Ising model, starting from it's RG equations:
$$\frac{d u_I}{dl} = 2 u_I + u_t^2$$
$$\frac{d u_t}{dl} = u_t$$
$$\frac{d u_h}{dl} =...
- 43
5
votes
1
answer
149
views
Why do we rescale momenta after integrating out high momenta in Wilsonian renormalization?
In Section 12.1 of Peskin & Schroeder they motivate Wilson's approach to renormalization by asking how a quantum field theory changes after changing the momentum scale. To answer this they start ...
- 3,900
1
vote
1
answer
352
views
Intuitive interpretation of the scaling dimension of an operator?
I am reading Field Theories of Condensed Matter Physics by Fradkin and in equation (4.10) it shows that an operator transforms irreducibly under scalings as
$$\phi_n(xb^{-1}) = b^{\Delta_n}\phi_x(x)$$
...
- 725
8
votes
0
answers
279
views
Fisher exponent and fractal structure
In the context of critical phenomena, there are several critical exponents commonly used to characterize the singular behaviour at the point of phase transition. The Fisher exponent $\eta$ is defined ...
- 518
2
votes
0
answers
50
views
What is the meaning of a non-canonical fixed point in the RG flow?
Consider, as an example, the Gaussian model:
$$
S[\phi]=\int\mathrm{d}\vec x\left[\frac{\gamma}{2}\left(\nabla\phi\right)^2+\frac{\mu^2}{2}\phi^2\right].
$$
RG analysis can be performed exactly by ...
- 83
3
votes
0
answers
137
views
Scaling limit, renormalization group and low-energy effective field theories
Given a quantum lattice theory $T_0$, e.g., in one dimension defined on $L$ sites, I know that there is a scaling limit, which introduces a lattice scale $a_0$ and keeps the following two quantities ...
- 823
5
votes
0
answers
116
views
Analytic change of free energy after renormalization
Suppose we have some model in statistical physics with Hamiltonian $H$ and partition function
$$Z=\mathrm{Tr}\left(e^{-H}\right) $$
the free energy per site is defined as
$$ f =\frac1N\log Z$$
A ...
- 4,776
3
votes
2
answers
330
views
Relating scaling and critical exponents in the Ising model
I'm reading the chapter about the renormalization group in Yeoman's book "Statistical mechanics of phase transitions" and I'm puzzled about how the author relates the scaling of the RG with ...
- 4,776
5
votes
1
answer
349
views
Identifying the relevant directions in the Ising model renormalization
I'm reading the chapter about the renormalization group in Yeoman's book "Statistical mechanics of phase transitions" and I'm puzzled about how the author relates the scaling of the RG with ...
- 4,776
3
votes
1
answer
220
views
Does the action remain dimensionless after the renormalization?
After the renormalization procedure, fields will gain an anomalous dimension, $\gamma$, which means that their scaling dimension will be different from what we would guess from the dimensional ...
- 33
4
votes
1
answer
294
views
Picture of poor man's scaling for AFM/FM interaction in Kondo problem
Poor man's scaling in Kondo problem
For the Kondo model:
$$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 ...
- 1,652
2
votes
1
answer
297
views
Anomalous dimension for 1D quantum Ising model
I am reading Chapter 10.2, Quantum Phase Transition--Subir Sachdev(P144), it said
All previous scaling dimensions of the d = 1 Ising model coincided with their so-called engineering dimension; the ...
- 1,652
4
votes
0
answers
49
views
Why/When would one study Renormalization Group flow of a system?
It is not that I am looking for a cheap way out of reading a book about RG flow, but I would like to know few key insights that RG flow study provides, backed with some specific examples. I know a ...
- 343
2
votes
1
answer
203
views
Why does the universe manifest scale?
I'll try outline my question in clear terms, articulating specific aspects that are its primary motivators. I'm just beginning in my exploration of physics as a student, but a persistent question that ...
3
votes
1
answer
119
views
confusion about what Wikipedia says about Renormalization
On the wikipedia page, on renormalization, it says the following: "Renormalization replaces the initially postulated mass and charge with new numbers such that the observed mass and charge matches ...
- 523
5
votes
1
answer
2k
views
Anomalous dimension for bare actions with a standard kinetic term
In this paper on p42, it is explained that when starting with a bare action that contains a standard kinetic term, this kinetic term attains a correction in the course of the RG flow which can be ...
- 9,691
5
votes
1
answer
576
views
Will Anderson's Poor Man's Scaling loose its effect when band width is small?
The s-d interaction Hamiltonian is as fellows
$H_I=Js.S$, J is the coupling strength.
We focus on the antiferromagnetic case, where $J>0$.
According Anderson's poor man's scaling, the ...
- 1,055
7
votes
2
answers
1k
views
What is the exact relationship between scale invariance and renormalizability of a theory?
I have often read that renormalizability and scale invariance are somehow related. For example in this tutorial on page 12 in the first sentence of point (7), self similarity (= scale invariance ?) is ...
- 9,691
10
votes
2
answers
1k
views
Why are conformal transformations so prevalent in physics?
What is it about conformal transformations that make them so widely applicable in physics?
These preserve angles, in other words directions (locally), and I can understand that might be useful. Also, ...
- 817