All Questions
14
questions
2
votes
0
answers
65
views
How to derive the long range behavior of XY model?
In a lecture note (Lec 23) by Sachdev (https://canvas.harvard.edu/courses/76589/files/folder/Lectures?), he considers a model
$$Z=\int D\theta(x)\,exp(-\frac{K}{2\pi}\int d^{2}x\,(\nabla_x\theta)^2),$$...
- 868
3
votes
0
answers
135
views
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 ...
4
votes
0
answers
514
views
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
0
answers
272
views
Conformal invariance and phase transitions?
At a second-order phase transition, a system exhibits fluctuations at any length scale. In such a scale-invariant regime, all the properties of the system follow specific scaling forms.
Close to a ...
- 314
1
vote
1
answer
208
views
Definition of linear and non-linear dynamic susceptibility
This question originates from the definition of linear and non-linear dynamic susceptibility in Uwe Tauber’s book “Critical Dynamics: A Field Theory Approach to Equilibrium and Non-Equilibrium Scaling ...
- 647
3
votes
0
answers
275
views
Correlation length and renormalization group
In Scaling and Renormalization in Statistical Physics there's following block of information:
I have some misunderstanding of some ideas.
1) How to define correlation length for arbitrary theory?
I ...
- 5,707
2
votes
1
answer
314
views
Various questions on renormalization in lattice systems
Forgive the long, multi questioned-question. The setting of this question is inspired by this answer.
Consider some theory on a lattice, for example the 2D $0$-field Ising model
$$H=-K\sum_{\langle i,...
- 4,736
4
votes
0
answers
252
views
Relation between scaling dimension and critical exponents for harmonic peturbations in $O(N)$ Wilson-Fisher (WF) in an old paper
I am reading the paper "Harmonic perturbations of generalized Heisenberg spin systems" (D J Wallace and R K P Zia, 1975) - https://iopscience.iop.org/article/10.1088/0022-3719/8/6/014/meta . The ...
- 41
3
votes
1
answer
792
views
Behavior in renormalization group flow that reaches critical point
First question. Does correlation length in renormalization group flow has to be infinite when it eventually reaches critical point?
Second question. Why does renormalization group flow keep partition ...
- 53
8
votes
2
answers
732
views
What's about the critical exponents and RG flow in upper critical dimension $D=4$?
We know when $D>4$, i.e. $D$ larger than upper critical dimension, then critical exponents are exactly same as the ones of mean field . When $D<4$, critical exponents are not given correctly by ...
user153663
3
votes
1
answer
1k
views
Critical exponents and scaling dimensions from RG theory
In most books (like Cardy's) relations between critical exponents and scaling dimensions are given, for example
$$ \alpha = 2-d/y_t, \;\;\nu = 1/y_t, \;\; \beta = \frac{d-y_h}{y_t}$$
and so on. Here $...
6
votes
2
answers
2k
views
The relation between critical surface and the (renormalization) fixed point
In the book, I read some remarks about the criticality:
Iterations of the renormalization (group) map generate a sequence of points in the space of couplings, which we call a renormalization group ...
- 3,691
1
vote
1
answer
467
views
Applicability of Cardy's "doubling trick" to the 2D Ising Model
In Section 11.2.2 of the book on Conformal Field Theory by di Francesco, Mathieu, and Senechal (page 417), the two point function on the Upper Half Plane is written as being equal to the four point ...
- 2,095
6
votes
1
answer
2k
views
Upper critical dimension in field theory
Is there field theory which describe a second-order phase transition without upper critical dimension? Mermin-Wagner says something about lower critical dimension but nothing about upper dimension.
- 981