All Questions
14
questions
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answers
38
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Calculation of conformal dimension for Ising model in two dimensional space
Recently I was reading Ph. Di Francesco's book, "Conformal Field Theory", and in section 7.4.2 where it discussed about Ising model, conformal dimensions $(h,\bar{h})$ are deduced from ...
1
vote
0
answers
85
views
Gaussian approximation of Landau Ginzburg and Renoramalization Group
I am studing an introduction to the Renormalization Group (RG); during my course my prof. came up saying that:
Landau-Ginzburg (LG) theory truncated at Gaussian order is exact at the critical point.
...
1
vote
0
answers
56
views
Landau Ginzburg path integral (PI) for the Ising model at gaussian order
I am stick with a problem in computing explicitely the gaussian PI in the Landau-Ginzburg theory for the Ising model.
If we do a procedure of coarse graining, we can define $m(x)$ as a continuous ...
5
votes
0
answers
275
views
Absence of Symmetry Breaking in 1D Ising Model--Continuum Version
I have seen arguments for why there is no symmetry breaking in the 1D Ising model--for example, using the transfer matrix method to explicitly solve the model, and another of energy-entropy arguments ...
- 642
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 ...
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
$$H=-K\sum_{\langle i,...
- 4,736
2
votes
1
answer
79
views
Critical parameter for 1D quantum system corresponding to $T_c$ of 2D Classical model
Utilizing the fact that there is a correspondence between a $d$ dimensional quantum system and a $d+1$ dimensional classical system (c.f. Trotter Decomposition), my question regards what the critical ...
- 3,710
4
votes
2
answers
2k
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How to understand the two-point correlation function in momentum space?
Let's take the Ising model as an example and study the
two point spin spin correlation function:
$$\langle s_0 s_r\rangle = \frac{\sum_{\{s_i\}}e^{K\sum_{\langle i ,j\rangle}s_i s_j} s_0 s_r}{\sum_{\{...
- 628
3
votes
2
answers
1k
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Transverse Ising model in continuum limit
Recently I have read "Analyzing the two dimensional Ising model with conformal fi eld
theory" by Paolo Molignini, but I don't understand clearly manipulations in the section about continuum limit of ...
- 2,664
2
votes
0
answers
303
views
Block diagonalizing a Hamiltonian using a symmetry
I have the following Hamiltonian, describing the 3 state Chiral clock model in 1D:
$$H = -f \sum_{j=1}^L (\tau_j^\dagger e^{-i \phi}+h.c.)-J\sum_{j=1}^{L-1}(\sigma_j^\dagger\sigma_{j+1}e^{-i\hat{\phi}}...
- 903
5
votes
1
answer
290
views
A question about the two-dimensional Ising model
The two dimensional square lattice Ising model reads
$$E[\sigma]=-J\displaystyle\sum_{<ij>}\sigma_i\sigma_j-h\displaystyle\sum_i\sigma_i,$$
where $E$ is the energy, $\sigma_i$ is the spin at ...
- 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
9
votes
1
answer
889
views
Temperature in the Hamiltonian limit
There is a well known connection between statistical mechanics in D spatial dimensions and quantum field theory in D-1 spatial dimensions. Changing the temperature in statistical mechanics corresponds ...
- 8,815
1
vote
1
answer
460
views
Topological entanglement entropy in transverse quantum Ising model?
I have seen from literature that the $Z_2$ lattice gauge theory in 2d could be mapped into a quantum Ising model with gauge constraints on the Hilbert space by dual transformation. The deconfined ...
- 421