All Questions
Tagged with lattice-modelising-model
41 questions
7votes
1answer
350views
Simple proof of a high temperature disordered phase for the Ising model
The original (and probably simplest) argument for the existence of an ordered phase for the Ising model at low (but non-zero) temperature was the Peirls argument, where you basically give an upper ...
3votes
0answers
60views
Correspondence between the Ising model considering vacancy and lattice gas
Several textbooks discuss the equivalence between the Ising model and the lattice gas. However, I have never seen a textbooks/article that discuss the correspondence between the Ising model with ...
2votes
1answer
121views
Ising model in a magnetic field (phase transition?)
I have some questions regarding the Ising model in the presence of a magnetic field which is non-uniform. Let us define the Ising Hamiltonian on a $d-$dimensional lattice, $$ H = -\frac{1}{2} \sum_{i,...
- 43
3votes
2answers
354views
Phase transition in Ising Model with local $\mathbb{Z}_2$ symmetry
I am studying the Ising model with a local $\mathbb{Z}_2$ gauge symmetry \begin{equation} \mathcal{H} = -\sum_{\text{plaquettes}} \sigma^z(\vec{x}, \vec{\mu})\sigma^z(\vec{x}+\vec{\mu}, \vec{\nu})\...
- 954
1vote
0answers
72views
Does the following generalization of the Ashkin-Teller model make sense
Ashkin-Teller (AT) model has interesting properties. I learned this from some threads here on PhysSE, particularly the recent one. In short, the AT model can be described as two layers of Ising spins. ...
- 6,933
5votes
0answers
211views
About 3D Ising model
In the 2D Ising model, Onsager provided an exact solution for the lattice model in 1944. However, despite numerous efforts, exact solutions for higher-dimensional Ising models have yet to be derived. ...
0votes
1answer
102views
Sampling a 2D Ising Model [closed]
I am fairly new to statistical mechanics and I am coming from a computing background. I am trying to calculate the mutual information of a lattice representing the 2D ferromagnetic Ising Model using ...
1vote
2answers
125views
Quantum Information Theory: How do I perform entanglement quantification calculations using the Quantum Heisenberg model?
I have been reading Quantum Computation and Quantum Information (10th edition) by Nielsen and Chuang and I am interested in calculating the level of entanglement (with entropy or some other measure I ...
- 23
4votes
1answer
229views
Duality relation for the correlation length
In this answer to my previous question, Yvan Velenik mentioned the equality for correlation lengths of dual Ising models on a square lattice $$ \xi(T) = \xi(T^*)/2. $$ I have the following questions ...
- 6,933
4votes
1answer
181views
Ising model rescaling
Consider the 2D classical Ising model. It's understood that there is a critical temperature $T_c$, and that the correlation length $\xi(T)$ defined by: $$\langle \sigma_i \sigma_j \rangle_\mathrm{...
- 7,115
2votes
1answer
322views
Di Francesco et al.'s CFT - additional corrections to free-energy for strip geometries on a lattice?
In classical spin systems, there's a nice way to extract the central charge of the model by looking at finite-size corrections to the free energy of strips of length $L$ and width $W$ in the limit of ...
- 2,472
1vote
1answer
93views
Non-translation invariant Gibbs state of the Ising model
In the book "Statistical mechanics of lattice systems" by Sacha Friedli and Yvan Velenik, on page 157 we have the following theorem concerning non translation invariant Gibbs states of the ...
- 909
0votes
1answer
100views
Ising model has short range correlation (Exercise in Velenik's book)
I'm studying the book "Statistical mechanics of lattice systems" by Sacha Freidli and Yvan Velenik, exercise 3.15 page 109: Let $\beta\geq 0$ and $h\in\mathbb{R}$, show that $\langle\cdot\...
- 909
0votes
0answers
78views
Local statistical model for percolation
I am interested in classical statistical models with degrees of freedom with a finite configuration set on regular lattices, and Boltzmann weights depending on the configurations in a constant-size ...
- 375
1vote
1answer
158views
Applications of real-space renormalizaton group (RG)
I'm looking for lattice models on which real-space RG can be applied fairly simply to get decent results. In particular, I'm looking for something like the classical 2D Ising model on a triangular ...
