All Questions
Tagged with spin-chains statistical-mechanics
25
questions
2
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Difference between boundary conditions in thermodynamic limit
Consider a model for a spin chain. I somehow am able to find a general formula for the expectation value of some observable in both periodic and open boundary conditions. ie.,
under PBC, I have
$\...
- 193
4
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0
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Are strong correlations of boundary spins possible in the absence of long-range order in the bulk?
Question about one-dimensional models with short range interaction of quantum spins, such as transverse Ising and Heisenberg models. Are there any examples when, in the ground state of the system, the ...
- 5,697
3
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1
answer
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Can a $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry generated by $\prod_{i} \sigma^x_i$ and $\prod_{i} \sigma^z_i$ be broken in a spin-$1/2$ chain?
I am interested in understanding patterns of spontaneous symmetry breaking in spin chains. I want to understand what happens when I have "competing" orders, like symmetry breaking orders ...
- 2,292
3
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1
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What is the signal of a spin wave?
From what I understand, for example in the Ising model, we can probe the correlation function via neutron scattering, and the correlation function gives the magnetic susceptibility for the system. Is ...
- 700
1
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0
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Parity of a 1d Ising model, and with higher order terms
I don't know if this should be asked here or in a math stack exchange, but I'll try here first.
Consider the classical 1d Ising model with periodic boundary condition:
\begin{equation}
H_2 (\vec{\...
- 368
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1
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Is there a name for a Heisenberg-like model, but instead of the ZZ operator, we have one that favor only spin-up-spin-up configurations?
I understand that the Quantum Heisenberg XXZ model in 1D has the form:
$$\hat H = \frac{1}{2} \sum_{j=1}^{N} (J_x \sigma_j^x \sigma_{j+1}^x + J_y \sigma_j^y \sigma_{j+1}^y + J_z \sigma_j^z \sigma_{j+1}...
- 700
1
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2
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169
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Mapping a 1D quantum Ising chain to a 2-dimensional classical Ising system
Going through Ref. 1 (I'll stick with the book's equation numbering), I'm learning about the mapping of quantum systems into classical systems. First of all let me briefly recap notation and some ...
- 1,989
5
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0
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474
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1D transverse-field Ising model - what is the difference between its classical and quantum treatment?
The 1D transverse field Ising model:
$$ H(\sigma)=-J\sum_{i\in Z} \sigma^x_i \sigma^x_{i+1} -h \sum_{i \in Z} \sigma^z_i$$
is usually solved in quantum way, but we can also solve it classically - ...
- 960
1
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170
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Correlation Functions of the one dimensional spin-1/2 XY Model
I am currently working on studying how to diagonalize the spin-1/2 XY model using the method included in " Annals of Physics 16.3 (1961): 407-466" by Lieb et al.
In fact, I'd like someone to ...
- 233
1
vote
1
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Correlation Functions: How can I prove this simple equation [closed]
The correlation functions of the Transverse Ising Model is beautifully explained in "Quantum Ising Phases and Transitions in Transverse Ising Models" Quantum Ising Phases and Transitions in ...
- 233
4
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0
answers
206
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Do magnons exist in 1D?
I'm confused about the state of a system described by the quantum Heisenberg model
$$ H = -J\sum_i \vec{S}_i \cdot \vec{S}_{i+1} $$
in 1 spacial dimension (1D spin chain). We can find the low energy ...
- 1,037
3
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0
answers
66
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Applications of spin models, integrability, and RG flows to information theory
As elucidated by E.T. Jaynes in his seminal papers, there is a deep connection between information theory and statistical mechanics.
The nature of my question is somewhat soft, so I apologise for that....
- 539
0
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2
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191
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What is the ground state wavefunction of $\hat{H}=-J\sum\limits_{\langle i,j\rangle}\hat{S}_i^z\hat{S}_j^z,~~ (J>0)$?
The hamiltonian of a collection of noninteracting quantum spin-$1/2$ operators $\hat{S}_i$ fixed at each lattice site $i(=1,2,..., N)$ in presence of magnetic field ${\bf B}=B\hat{{\bf z}}$ $$\hat{H}=-...
- 26.8k
3
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1
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(Transverse) Ising Model Higher Than Four Dimensions
First question:
Wiki says Ising Model higher than four dimensions can be described by mean field theory. What is the reason for this? Does this mean there is no phase transition for higher dimensions ...
- 470
1
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0
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Generalised Ising models?
Are there generalised Ising models:
The underslying mesh/connectivity is completely arbitrary - non rectangular, 3D...ND, complete connectivity should be possible
The interaction potential is ...
- 273