All Questions
Tagged with spin-models mathematical-physics
11
questions
7
votes
1
answer
209
views
Why is $H = J \sum_i (S^x_i S^x_{i+1} + S^y_iS^y_{i+1})$ always gapless for any spin $S$?
In the following I have in mind antiferromagnetic spin chains in periodic boundary conditions on a chain of even length $L$.
Consider the spin-$S$ spin chain
$$H = J \sum_{i=1}^L (S^x_i S^x_{i+1} + S^...
- 2,292
2
votes
0
answers
45
views
How to show random cluster models with non-integer $q$ have no local description?
It is known that the random cluster model with $q = 1$ corresponds to bond percolation, and $q = 2, 3, ... $ corresponds to the $q$-state Potts model. Both of these have a local description.
What ...
- 49
1
vote
1
answer
57
views
Is the random current model tight (in the sense of probability)?
Let us consider the random current model (of the classical Ising model) on $\mathbb{Z}^d$. More specifically, we have probability measures $\mathbb{P}_L$ on the product space $\mathbb{N}^{E_L}$ where $...
- 2,123
1
vote
0
answers
59
views
Holley and FKG Lattice Conditions
There's an interesting exercise (page 13, Exercise 11) in Hugo Duminil-Copin's Lectures on the Ising and Potts models on the hypercubic lattice, which states that the following 2 statements are ...
- 2,123
2
votes
0
answers
61
views
(In)finite lattice in quantum statistical mechanics: validity of phase classifications and TQFT [closed]
I would like to understand the motivation for studying quantum statistical mechanics, such as spin models, on an infinite lattice, or in other word, in the operator algebraic framework. I learned that ...
- 115
4
votes
0
answers
68
views
Minor details of Mermin-Wagner
In the proof of Mermin-Wagner (e.g., scholarpedia), there is a minor assumption that the average magnetization $m_\Lambda (h)$ converges in the thermodynamic limit $\Lambda \to \mathbb{Z}^d$ to some $...
- 2,123
1
vote
1
answer
173
views
Why is the sequence of limits $\lim\limits_{V\to\infty}\lim\limits_{B\to 0}m(B,V)$ when reversed does not give the same result?
For spontaneous magnetization $m$ in a sample of volume $V$, what do the limiting operations $$
\lim\limits_{V\to\infty}\lim\limits_{B\to 0}m(B,V)=0,\\
\lim\limits_{B\to 0}\lim\limits_{V\to\infty}m(B,...
- 11.8k
0
votes
0
answers
69
views
Order parameter fluctuations in the mean field model for ferromagnetism (mathematical approach)
I'm a math student taking first steps into statistical mechanics and... I need help!
Consider the Curie-Weiss model (i.e. the classical mean field model for ferromagnetism). If $N$ is the number of ...
- 1
1
vote
0
answers
55
views
3d spatial string-net model and its plaquette term
Can someone explain the following sentence, saying the difference betweeen the 2d string-net plaquette intersections and 3d string-net plaquette intersections?
Thus, for 3d sting-net model, if
we ...
user32229
0
votes
0
answers
214
views
A simple question on the projected wave function?
For example, consider a spin-1/2 AFM Heisenberg Hamiltonian $H=\sum_{<ij>}\mathbf{S}_i\cdot\mathbf{S}_j$, and we perform a Schwinger-fermion($\mathbf{S}_i=\frac{1}{2}f^\dagger_i\mathbf{\sigma}...
- 3,744
26
votes
1
answer
1k
views
Mermin-Wagner theorem in the presence of hard-core interactions
It seems quite common in the theoretical physics literature to see applications of the "Mermin-Wagner theorem" (see wikipedia or scholarpedia for some limited background) to systems with ...
- 10.5k