Tagged Questions
1
vote
1answer
105 views
Renormalization Group and Ising with d=1 and D=1
I have a question about the results of RG on Ising model. I know it's possible to obtain two couple of relations
$K'(K)$, $q(K')$
$K(K')$, $q(K)$
between the coupling costants. My problem arise ...
4
votes
0answers
73 views
Drawing the RG flow diagram
In real-space renormalization group how does one find the complete RG flow exactly, (not schematically)? I understand it needs to be done on a computer. For example, I have the ising model on a ...
4
votes
0answers
69 views
Exact Beta Functions in Statistical Mechanics
I'm looking for analytically solvable models in statistical mechanics (classical or quantum) or related areas such as solid state physics in which
the beta function for a certain renormalization ...
2
votes
1answer
67 views
What is the physical meaning of this simplification to calculate the effective coupling constants for a Gaussian model with quartic interactions?
To calculate the effective coupling constants $u'_2(q)$ and $u'_4(q)$ of the effective Hamiltinian eq (4.9) of this paper
$$ H' = -\frac{1}{2}\int\limits_q u'_2(q)\sigma'_q\sigma'_{-q}
- ...
2
votes
0answers
99 views
Nonpertubative renormalization in quantum field theory versus statistical physics
I am trying to work my head around how renormalization works for quantum field theory. Most treatments cover perturbative renormalization theory and I am fine with this approach. But it is not the ...
4
votes
1answer
201 views
Reasons for violation of universality in statistical mechanics
The Universality in statistical mechanics is nicely explained by the renormalization group theory. However, there are fair amount of numerical and theoretical studies show that it can be violated in ...
3
votes
1answer
78 views
Freedom in the Choice of a Beta Functions in RG
Assume we're given a certain statistical model, say the infinite range Ising model
\begin{equation}
H_{N}\{\vec\sigma_{N}\}~=~ - \frac{x_{N}}{2N} \sum_{i,j =1}^{N} \sigma_{i} \sigma_{j}
...
2
votes
1answer
111 views
renormalization group in d=3
Do we really understand why the renormalization group in $d=2+\varepsilon$ and $d=4-\varepsilon$ taking $\varepsilon=1$ gives "good" values for critical exponents in $d=3$? Are they exceptions?
Is it ...
2
votes
1answer
103 views
What's the meaning of the coupling change after a renormalization (in the 1-dim Ising Model)?
What does it mean that after the theory (1-dim Ising model here, but the question is general) is renormalized one time and $g_i\rightarrow g_i'$, that the couplings are weaker, even if the theory ...
3
votes
1answer
168 views
Scaling with the Ising Model
I am stuck with one formula in the CFT book by Di Francesco and al. Chapter 3. Equation 3.46 third step, for those who don't have the book, he integrates out degrees of freedom from the Ising Model by ...
0
votes
1answer
101 views
Renormalization Group for anisotropic “Gaussian” model
I'm considering an "anisotropic" Hamiltonian of the form
$$\beta H = \int d^n r_{||} d^{d-n} r_{\bot} \frac{K}{2} (\nabla_{||} m)^2 + \frac{L}{2} (\nabla^2_\bot m)^2 + \frac{t}{2}m^2 - hm$$
which in ...
4
votes
1answer
254 views
Renormalization Group: Different fixed points
Extending the Gaussian model by introducing a second field and coupling it to the other field, I consider the Hamiltonian
$$\beta H = \frac{1}{(2\pi)^d} \int_0^\Lambda d^d q \frac{t + Kq^2}{2} ...
0
votes
2answers
143 views
RG of the Gaussian Model: Finding the scaling factor
I'm studying how the Renormalization Group treatment of the simple Gaussian model,
$$\beta H = \int d^d r \left[ \frac{t}{2} m^2(r) + \frac{K}{2}|\nabla m|^2 - hm(r)\right]$$
In momentum space, the ...
2
votes
2answers
291 views
Identifying a critical phenomena?
I have a system with a number of measurables (in time). Some measurables are discrete some are continuous (within the measurement accuracy). How can I determine whether my system experiences ...
2
votes
1answer
74 views
Why is $\rho_m$ proportional to the deviation from critical temperature in critical phenomena?
In Peskin and Schroeder's chapter 12 about the renormalization group, it is stated that the parameter $\rho_m=m^2/M^2$, where $m$ is the mass and $M$ is the renormalization scale, is proportional to ...
