All Questions
16
questions
2
votes
0
answers
53
views
Are there universality classes not found through a Ginzburg-Landau like free energy expansion
Usually the real free energy of a system is too complex to be exactly computed, thus one either expands it in power/gradient series or simply builds it from symmetry considerations. For example:
$$F[\...
- 1,168
3
votes
0
answers
77
views
Question about statistical field theory
I am starting to learn statistical field theory. The "infinite number of degrees of freedom" refers to the continuous nature of field variables in field theory, where there are infinitely ...
user347949
8
votes
1
answer
279
views
Assumptions behind the Quantum Master Equation derived using Batalin-Vilkovisky Formalism
Is there any underlying assumption(s) behind the Batalin-Vilkovisky Quantum Master Equation:
$$\frac{1}{2}(S,S) = i\hbar\Delta(S)~?$$
As an example, if we consider the Nakajima–Zwanzig Master Equation,...
- 756
3
votes
0
answers
61
views
Can the upper and lower critical dimensionalities of a model coincide?
Is it possible for a field theory to have the same upper and lower critical dimensions? Has this ever been observed in any model (be it condensed matter, statistical mechanics, QFT, string etc.)?
- 71
2
votes
0
answers
346
views
Scaling dimension in statistical field theory
I got stuck in understanding the scaling dimension in statistical field theory. Currently I am reading the statistical field theory written by Prof. David Tong. In his note(p.63), it states that the ...
- 413
2
votes
0
answers
62
views
Convergence of Gibbs Measures
(I restrict my question to nearest-neighbor models for simplicity)
Let $\Lambda$ be a finite subset of $\mathbb{Z}^d$ and $E$ be the set of nearest neighbor edges where both vertices lie within $\...
- 2,024
1
vote
0
answers
70
views
Fluctuation-Dissipation Relation for Quantum Phase Transitions
I am looking for a formulation for the fluctuation-dissipation relation connecting the correlation related quantities with the thermodynamic functions at the quantum critical point.
The fluctuation-...
- 646
2
votes
1
answer
93
views
Generalized Ising model
I am in very trouble with a particular expression. I leave the original pages in order to have everything available and what I am goin to leave are the first pages of nine chapter of Non Perturbative ...
1
vote
0
answers
41
views
Physical Interpretation of Partition Function with Background Field
Integrals of the form
$$\langle{\phi(x_1)\cdots\phi(x_n)}\rangle=\frac{1}{Z}\int\mathcal{D}\phi\,e^{-\frac{1}{\hbar}S(\phi)}\phi(x_1)\cdots\phi(x_n)$$
can be evaluated by considering Feynman diagrams ...
- 3,915
3
votes
1
answer
248
views
Rescaling of effective hamiltonian coupling constants in the Wilsonain renormalization group
I am confused about an aspect of coupling constant rescaling in the Wilsonian renormalization group procedure. (I'm following Kardar's "Statistical Physics of Fields, Ch5). I think I understand the ...
- 63
1
vote
1
answer
201
views
Second quantisation for fermions
I am trying to build a model for reactions on a lattice in the Doi-Peliti formalism. Suppose there exists a lattice of $N$ sites indexed by $i$. Each site can be either occupied or unoccupied. ...
- 141
3
votes
1
answer
1k
views
Critical exponents and scaling dimensions from RG theory
In most books (like Cardy's) relations between critical exponents and scaling dimensions are given, for example
$$ \alpha = 2-d/y_t, \;\;\nu = 1/y_t, \;\; \beta = \frac{d-y_h}{y_t}$$
and so on. Here $...
3
votes
1
answer
625
views
Why do we rescale and renormalize fields?
The Renormalization procedure is generically broken down into three steps (see eg Kardar Statistical Fields Chapter 4)
1) Coarse Grain (Typically this amounts to integrating out the fast Fourier ...
- 2,270
1
vote
0
answers
84
views
Functional Gaussian Integral Involving Gradient Square with non-trivial Kernel
I have been trying to solve the following functional gaussian integral. I've had problem finding the inverse kernel. $f(x)$ and $\rho(x)$ are two known scalar fields and they do vanish at infinity.
$...
- 83
1
vote
1
answer
195
views
Mean free path in QFT
I'm trying to understand the hydrodynamic approximation of a general QFT when the large $k$ and $\omega$ DOF have been integrated out i.e that at highly enough temperature every non-trivial QFT ...
- 145