All Questions
Tagged with spin-models critical-phenomena
18
questions
2
votes
0
answers
44
views
Equivalent definitions of (dis)continuous phase transitions at criticality
Consider a classical lattice model on $\mathbb{Z}^d$ and suppose that the system undergoes a phase transition as you lower the temperature, i.e., increase $\beta$. The most general definition of a ...
- 2,113
0
votes
0
answers
69
views
Two-dimensional Ising model for square lattices
Consider Onsager's exact solution of two-dimensional Ising model for square lattices with nearest neighbour interaction energy ‘J ‘being equal in the horizontal and vertical directions. At the ...
- 1
2
votes
1
answer
255
views
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
2
votes
0
answers
41
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How can I find the critical dimension for the Blum-Capel model near the tricritical point in mean field theory?
I believe that I have found the critical dimension for the critical temperatures on the critical line (that is, where the second order phase transition occurs), which is $D=4$. This is because the ...
- 185
6
votes
2
answers
1k
views
At the critical point, is Kramers-Wannier duality a unitary symmetry of the model?
I have in mind the transverse ising model and its (self-dual) generalizations, such as
$$H_{TI} = \sum_i \sigma^z_{i}\sigma^z_{i+1} + h \sigma^x_{i}$$
and
$$H_{SDANNI} = \sum_i (\sigma^z_{i}\sigma^z_{...
- 2,282
5
votes
2
answers
303
views
Two lines of critical points described by CFTs with different central charges intersect. What happens?
There is a lovely set of two-parameter spin chains that can be mapped to quadratic fermions and studied quite exactly:
$$H = -\sum_{i} \frac{1+\gamma}{2}\sigma^x_i\sigma^x_{i+1}+\frac{1-\gamma}{2}\...
- 2,282
6
votes
1
answer
543
views
Log-law entanglement with large central charge contradict bounds on the entanglement entropy
I am trying to learn more about entanglement entropy in large but finite-size systems at critical points. I am still relatively new to conformal field theory, so it is not unlikely I have ...
- 2,282
2
votes
1
answer
723
views
Proof of Mermin-Wagner Theorem
There are many presentations of the proof of the Mermin-Wagner theorem in many different contexts (which talk about quantum vs. classical, existence of unique Gibbs measure or non-zero mean ...
- 2,024
0
votes
1
answer
118
views
What is this model? [closed]
Consider the following model in classical statistical mechanics. Take a finite box $\Lambda\subseteq\mathbb{Z}^d$ and consider the field $\phi:\Lambda\to[-1,1]$ whose Gibbs measure is given by $$ \...
- 2,024
2
votes
0
answers
28
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Is there existing research suggesting that critical systems' power spectra are correlated with their eigenspectra?
I am interested in how the spatial and temporal spectral exponents – in other words the exponents of the power spectrum and eigenspectrum – of a high dimensional system at criticality are related. It ...
- 121
4
votes
2
answers
441
views
What is short-range antiferromagnetic order?
I know what anti-ferromagnetism is. But in a paper I came across "short-range antiferromagnetic order". Can someone please explain to me what it is.
- 399
2
votes
0
answers
95
views
What is the critical temperature for a BKT transition in the 2D quantum XY model with $S=1$ (not $S=1/2$)?
What is the critical temperature for a BKT transition in the 2D quantum XY model with $S=1$ (not $S=1/2$)? For instance, the classical XY model has KTc/J = 0.898 and the quantum XY model with S=1/2 ...
- 21
9
votes
2
answers
519
views
Integrability of a non-integrable quantum spin model at critical point
Is it right, that non-integrable quantum spin models in one dimension become integrable at their critical points? Or do they stay nonintegrable at the critical point also? Are there any examples known?...
- 5,687
1
vote
0
answers
499
views
Why the correlation function of 2D classical XY model is written so?
2D classical XY model $$H = -J\cos(\theta_{i}-\theta_{j})%$$ is famous for Berezinskii-Kosterlitz-Thouless phase transition. This is because of the difference of correlation function between hot and ...
- 61
2
votes
0
answers
68
views
How to quantify frustration for spin models with long range interactions?
Consider the following Hamiltonian:
$$
H=-\sum_{i\neq j}J_{ij}S_iS_j-\sum_i H_iS_i
$$
where $S_i\in\{-1,1\}$, and the summed pair $i,j$ can be any two distinct indices (not necessary adjacent spins)....
- 713