All Questions
Tagged with spin-models critical-phenomena
18
questions
9
votes
2
answers
522
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?...
8
votes
2
answers
358
views
Is there a spin glass version of Prince Rupert's Drop?
Spin Glasses are known to converge to their ground state under Simulated Annealing.
The word choice is especially interesting since annealing is also the name of a process performed on actual glass. ...
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
$$H_{SDANNI} = \sum_i (\sigma^z_{i}\sigma^z_{...
6
votes
1
answer
550
views
Log-law entanglement with large central charge contradict bounds on the entanglement entropy
I am trying to learn more about entanglement entropy in large but finite-size systems at critical points. I am still relatively new to conformal field theory, so it is not unlikely I have ...
5
votes
2
answers
307
views
Two lines of critical points described by CFTs with different central charges intersect. What happens?
There is a lovely set of two-parameter spin chains that can be mapped to quadratic fermions and studied quite exactly:
$$H = -\sum_{i} \frac{1+\gamma}{2}\sigma^x_i\sigma^x_{i+1}+\frac{1-\gamma}{2}\...
4
votes
2
answers
448
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.
2
votes
1
answer
729
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
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 ...
2
votes
0
answers
45
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
votes
0
answers
42
views
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 ...
2
votes
0
answers
28
views
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 ...
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 ...
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)....
1
vote
1
answer
1k
views
Why is the critical exponent $\alpha$ negative at the Ising spin-glass transition?
The specific heat usually diverges at a phase transition - typically as a power-law, giving a critical exponent $\alpha > 0$. (Although in 2D, sometimes the divergence is only logarithmic, as with ...
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 ...