All Questions
Tagged with renormalization critical-phenomena
58
questions
2
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0
answers
45
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Universality and continuous variation of critical exponent close to a tricritical point
A tricritical point is a point at which a second order transition line and a first order transition line merge.
At equilibrium, this point can be described by a landau potential (see for example this ...
- 1,168
4
votes
2
answers
190
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Role of the natural temperature scale in the anomalous dimension of the renormalization group
In David Tong's lecture notes on statistical field theory, the concept of anomalous dimensions is introduced by considering the scaling of the correlation function $$\langle \phi(\mathbf{x}) \phi(\...
- 307
3
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0
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59
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Can the Wilson-Fisher fixed point be reached from the massless $\phi^4$ action?
Most textbooks and papers work out the derivation of the Wilson-Fisher fixed point for $\phi^4$ starting from the massive action (in Euclidean space)
$$S = \int d^d x \biggl( \frac{1}{2} \partial_\mu \...
- 1,723
3
votes
2
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64
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Anomalous dimension must be positive in Ginzburg-Landau $\phi^4$-like theories?
I am trying to understand/find the argument behind a claim made in this paper (page 3, column 1): that the anomalous dimension/exponent $\eta$ of a continuous phase transition in Ginzburg-Landu $\phi^...
- 636
1
vote
1
answer
60
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New Universality Classes and Multiple Transition Points in Systems [closed]
I'm currently exploring several concepts related to universality classes, phase transitions, and critical phenomena. My questions revolve around the comprehensiveness of universality classes, the ...
- 167
7
votes
2
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936
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Is renormalization different to just ignoring infinite expressions?
Looking into textbooks, I got the impression in renormalization perturbation theory one adds
counterterms to the Lagrangian to cancel terms (usually integrals) that are infinite.
My question is, could ...
- 89
1
vote
1
answer
112
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Is the lattice spacing $a$ a dangerously irrelevant parameter?
Near a renormalization group fixed point, we can perform a scale transformation of length $L' = b^{-1} L$. In this case the relative lattice spacing should transform as $a' = b^{-1} a$. After $n$ ...
- 164
1
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0
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110
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Extra term in $2+\epsilon$ expansion of sigma model
I'm working through David Tong's notes on Statistical Field Theory, in particular the $2+\epsilon$ expansion of the sigma model with free energy
$$F[\vec{n}]=\int d^dx \frac{1}{2e^2}\nabla\vec{n}\cdot\...
- 248
2
votes
1
answer
255
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How renormalization allows to describe critical point behaviour using the critical fixed point?
As in the title, I am trying to understand how the critical fixed point (CFP) can be used to derive the thermodynamic singular behavior of the physical critical point (PCP). The context I have in mind ...
- 823
4
votes
1
answer
225
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Connection between the $\beta$-function and critical exponents
In my recent readings in QFT, I came across the fact that there is a connection between critical exponents in thermodynamics and the $\beta$-function of the renormalization group flow. Does anybody ...
- 531
3
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answers
135
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Zeros of multiplicative wave function renormalization
It is probably needless to recall here that the Reimann zeta function $$\zeta(s)=\sum_{n=1}^\infty n^{-s}$$ and its generalizations are among the central objects of study in mathematics.
The main open ...
0
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47
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Dynamical critical exponent in stochastic vector model
For stochastic $O(N)$ model given by:
$$S[\psi,\phi]=\int \frac{d\omega\, dk^D}{(2\pi)^{D+1}} \left( \vec{\psi}(-k,-\omega).\vec{\phi}(k,\omega) \left(-i\omega + \gamma k^2+r \right) -2T\vec{\psi}(-k,-...
- 1,417
2
votes
1
answer
93
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"Quantum" hyperscaling relation from a Renormalization Group (RG) viewpoint
Through the RG method, one can obtain the hyperscaling relation between the critical exponents of classical second-order phase transitions:
\begin{equation}
2-\alpha=\nu d
\end{equation}
In the case ...
- 1,396
4
votes
0
answers
515
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Connection Between Renormalization Group and Phase Transitions
I have a couple of questions on the relation of RG and phase transitions. I've heard in many sources that the theory of most transitions (excluding novel phase transitions like Quantum Critical ...
- 642
1
vote
1
answer
298
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Dimensionless vs. dimensional RG-Flow equations
When one writes down RG-Flow equations for any theory, at some point one encounters statements like
"It is useful to properly rescale the above exact flow equations and rewrite them in ...
- 324