Questions tagged [spin-models]
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150
questions
5
votes
0answers
56 views
Gilbert original paper (1955) reference
I'm looking for the Gilbert's original paper where he derives the gyromagnetic Landau Lifshitz Gilbert (LLG) equation of motion from a variational principle.
Most of the people cite:
Gilbert, ...
1
vote
0answers
16 views
Why do the Binder Cumulants of different system sizes intersect at the critical point?
When Monte Carlo simulations are performed for spin models (Ising model etc.) the critical temperature can be found by simulating for different lattice sizes and plotting the Binder Cumulant for them. ...
1
vote
0answers
17 views
Why the geometrical frustration (spin ice model) has never been studied in superparamagnetic size range?
I'm trying to understand the effect of geometrical frustration in assembly of superparamagnetic nanoparticles but I can't find any reference. Does anyone know how magnetism can be affected by ...
1
vote
2answers
46 views
Different concepts of phase transitions in spin models
I am currently revising the lecture notes in which different spin systems
are analyzed, focussing on the occurrence (or absence) of phase transitions.
Different techniques are applied to analyze the ...
1
vote
0answers
20 views
Semiclassical limit $S \to\infty$ in spin model
In many literature, the limit $S \to \infty$ is considered as a semiclassical limit. My question is that when this approximation is valid? Since paticles, say electrons, have the fixed spin number $S=...
0
votes
1answer
45 views
Spinmodel Statistics
Consider a spin model with the following energy with $ \{\sigma\} =(\sigma_1,\sigma_2,...,\sigma_N)$ where each $\sigma$ can take the values: $-s,-s+1,...,-1,0,1,...,s-1,s$ and $E(\{\sigma \}) = \mu H ...
0
votes
0answers
16 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 ...
0
votes
1answer
30 views
Swap operation with the Heisenberg Hamiltonian
According to REF 1 equation 3, a SWAP operation can be achieved via the Heisenberg Hamiltonian for spins $H=J(t)\mathbf{S}_1\mathbf{S_2}$
$U^{1/2}_{SWAP}=e^{-i\frac{\pi}{8}}\exp\left(i\frac{\pi}{2}\...
1
vote
0answers
18 views
Is it possible to implement the Invaded Cluster Algorithm on a network of Ising spins rather than a lattice?
My main concern is how to know if a cluster has percolated the network. For a periodic square lattice it is easy to determine if the cluster percolates by looking at the size of the cluster (as given ...
0
votes
0answers
43 views
Troubles with Haldane Shastry Spin Chain
I'm actually reading the article of Shastry "Exact solution of an S= 1/2 Heisenberg Antiferromagnetic Chain with Long-rnaged interactions", Phys.
Rev. Lett. 60, 639 (1988)"
The articles ...
1
vote
0answers
22 views
Cavity method pedagogic references
I am looking for pedagogic references (textbook, review/expository articles, lecture notes, etc.) explaining the cavity method in detail.
I am talking specifically about this:
https://link.springer....
5
votes
1answer
152 views
Symmetry transformations that are self-inverse and global symmetries of the Hamiltonian
I have the simplified Ising model. The Hamiltonian is given by
$$
\mathcal{H} = -\mathrm{J}\sum_{<ij,i' j'>} \sigma_{ij} \sigma_{i'j'}.
$$
Where the sum over $<ij,i'j'>$ means just the ...
5
votes
1answer
76 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?...
0
votes
1answer
64 views
Bose-Einstein distribution and magnons
I have some doubt about the Bose-Einstein distribution for magnons/spin-waves.
A one-dimensional ferromagnet placed in an external magnetic field $\mathbf{B} = B\, \hat{z}$ obeys the Hamiltonian
$$H ...
0
votes
0answers
65 views
Why the correlation function of 2D classical XY model is written so?
2D classical XY model $$H = -J\cos(\theta_{i}-\theta_{j})%$$ is famous for Berezinskii-Kosterlitz-Thouless phase transition. This is because of the difference of correlation function between hot and ...
1
vote
1answer
100 views
Two spin-1 system and the projector onto total spin 2 subspace [closed]
I am having trouble grasping the projection operators in the context of composite spins system, e.g. with two spin-1. First off, a projector $P$ is said to be an operator that squares to itself, $P^2=...
1
vote
0answers
16 views
In spin systems, a mean field with nonzero Chern number after Gutzwiller projection changed into trivial state?
The mean field is nontrivial because of nonzero Chern number. The gauge symmetry is Z2. Under Gutzwiller projection, I calculate the ground state degeneracy(GSD) and find that the GSD is one(trivial ...
0
votes
1answer
189 views
What is the Kitaev Model and why it became so popular? [closed]
I am seeing Kitaev Model everywhere. It feels like the spin-glass model of our time. How the Kitaev model differ from spin-glass and why it can be used everywhere? Looking at equation 1 here suggests ...
1
vote
0answers
34 views
How can I compute the spin texture for a $SU(2)$ gauge model?
I am trying to determine the helicity of 4 Dirac cones in my model, and one way I want to approach it is by plotting the spin-texture. However, I am unsure of how one would calculate the spin-texture ...
0
votes
0answers
61 views
spinless and time reversal symmetry breaking of p-wave pairing in topological superconductors
In the context of Majorana zero modes, I often hear that the p-wave pairing is effectively 'spinless' and time reversal symmetry broken.
I understand that s-wave and p-wave refer to the spin portion ...
2
votes
0answers
37 views
How to quantify frustration for spin models with long range interactions?
Consider the following Hamiltonian:
$$
H=-\sum_{i\neq j}J_{ij}S_iS_j-\sum_i H_iS_i
$$
where $S_i\in\{-1,1\}$, and the summed pair $i,j$ can be any two distinct indices (not necessary adjacent spins)....
1
vote
1answer
89 views
One-dimensional $SU(3)$ Heisenberg Model, the non-linear sigma model, $\theta$-term
Let's consider a one dimensional $SU(N)$ antiferromagnetic Heisenberg Model with an irreducible representation and its conjugate on alternating sites, such that they correspond to a Young tableaux ...
1
vote
1answer
87 views
What is the order parameter of 2D generalized $XY$ model?
I'm now studying the phase transition of 2D generalized XY model. This model considered here has a mixture with ferromagnetic and nematic-like interactions,
$$\mathcal{H}=-\sum_{\langle i j\rangle}\...
1
vote
0answers
75 views
How to find groundstate energy of a simple Hamiltonian at $N/L$-filling using Jordan-Wigner (JW) transformation?
$\underline{\textbf{Model:}}$
Let we have the $t-V$ model for spinless fermions on a 1D lattice, which is defined in second quantization operators as follows:
$$H_1 = -t\sum_i \big(c_i^\dagger c_{i+...
0
votes
1answer
75 views
What are exactly “norms” in spin networks? Are there any non-quantum spin networks?
Roger Penrose proposed a series of networks from which, fundamentally, space-time would emerge, called spin networks
(https://en.wikipedia.org/wiki/Spin_network)
In this article, it is said:
...
0
votes
0answers
20 views
Exchange stiffness for HCP
I am studying the exchange interaction, which can be described with the Heisenberg Hamiltonian:
$\hat{H} = -\sum_{i,j}J_{ij}\hat{\mathbf{S_i}}\cdot \hat{\mathbf{S_j}}$
In the framework of constant ...
1
vote
0answers
27 views
$p$-spin spherical spin glass
Consider the $p$-spin spherical spin glass model with Hamiltonian $$H_{N,p}(\sigma)=\frac{1}{{N}^{\frac{(p-1)}{2}}} \sum \limits_{i_1,...i_p} J_{i_1,...i_p} \sigma_{i_1} \sigma_{i_2} .. \sigma_{i_p} $$...
0
votes
0answers
41 views
Which phenomenon is related to the spin of photons? [duplicate]
The phenomenon of the deflection of a moving electron in a magnetic field is related to the electrons spin. From which phenomenon it is concluded, that photons have a spin?
0
votes
1answer
143 views
Relation between spin and polarization of photon? [duplicate]
What is the possible spin configuration of photon?
And does spin has any relation with polarization?
1
vote
1answer
48 views
A dreidel on a spinning table
In the spirit of the holidays.
Let's assume that a dreidel is spinning counter-clockwise at frequency $f$ on a table.
From external point of view, what will I see if I rotate the table clockwise at ...
0
votes
1answer
62 views
Average entropy of a subsystem
In this paper by Don Page, https://arxiv.org/pdf/gr-qc/9305007.pdf, He conjectures average entropy of a substem of dimension m with Hilbert space dimension mn, $m \leq n$. to be :
$ S_{mn} = \sum_{n+...
0
votes
2answers
222 views
Pauli matrices as measurement operators versus spin probability
Pauli matrices tell us what the spin of a particle is along a certain axis.
Let's say I want to measure the spin along the z-axis then the pauli operator
$$\sigma_z = \begin{bmatrix}1&&0\\0&...
1
vote
2answers
395 views
Finding the Eigenvalues and Eigenvectors of the Hamiltonian for three spin-1/2 particles coupled antiferromagnetically
Problem
Given three spin-1/2 particles with the total spin operator $\vec{S}=\sum\limits_{i=1}^3 \vec{S}_i$ and its $z$ projection $S_z=\sum\limits_{i=1}^3 S_{z,i}$, and the Hamiltonian
$$H = J\sum\...
1
vote
0answers
27 views
Discrepancy regarding Husimi Probability distribution calculation
I am trying to simulate a system of j qubits and for visualization of the dynamics considering the Husimi distribution of the state.
To carry out the projection onto coherent states I have proceeded ...
1
vote
1answer
38 views
Constructing PEPS representation of an arbitrary quantum state
Given a quantum state we can construct its MPS (Matrix Product State) representation by doing a series of singular value decompositions. Given the freedom to choose arbitrary bond dimensions the MPS ...
2
votes
1answer
136 views
Integrability of generalized Richardson-Hubbard model
Recently I got a bit interested in the possibility of finding spectrum of few interesting class of lattice quantum mechanical hamiltonians like Richardson's pairing hamiltonian, 1D Hubbard hamiltonian,...
1
vote
1answer
59 views
Microscopic and macroscopic description of spin waves
Hamiltonian
Consider the one-dimensional Heisenberg ferromagnet specified by the Hamiltonian
$$H = -\frac{|J|}{2}\sum_{i,\delta} \mathbf{S}_i\cdot \mathbf{S}_{i+\delta}.$$
Here $i$ labels the spin ...
1
vote
0answers
56 views
Self-modifying Hamiltonians (Lagrangians) and emerging intelligence? [closed]
Are there dynamical physical systems that are governed by self-modifying Hamiltonians (Lagrangians), i.e. Hamiltonians (Lagrangians) determine not only the next point in phase space, but also the form ...
1
vote
1answer
56 views
Reduced density matrix of the edge spin-1/2 in AKLT spin chain
I am trying to understand the paper titled, "Entanglement in a Valence-Bond-Solid State" by Fan, Korepin, and Roychowdhury (https://arxiv.org/abs/quant-ph/0406067).
I was able to understand the ...
3
votes
2answers
154 views
How can I say whether a Hamiltonian is integrable or not?
The transverse field Ising Hamiltonian $$ H = J\sum_{i=0}^{N}\sigma_{i}^{z}\sigma_{i+1}^{z}+h_{x}\sum_{i=0}^{N}\sigma_{i}^{x} $$ is integrable because it can be exactly solved using Jordan Wigner ...
2
votes
0answers
66 views
Elitzur theorem and the Ising model
I was recently studying the Elitzur theorem and its application to the Ising model on Kogut: An introduction to lattice gauge theories and spin systems, chapter $5$C. I was wondering how he obtain $\...
2
votes
1answer
100 views
Physical Realization of Three-Level System
I have come across the Hamiltonian (where $\varepsilon,\Delta\geq0$) in one of my problem sets:
$$H=
\left(\begin{array}{c c c}
0&0&0\\
0&\varepsilon-\Delta&0\\
0&0&\...
1
vote
0answers
78 views
Practical/experimental difference between (quantum) Heisenberg and (classical) Ising model
I have read a few discussions about the difference between the Heisenberg model (using quantum spin operators) and Ising model (with spins $\pm 1$), notably this one or this Quora post.
All the ...
1
vote
1answer
85 views
About spin chain string order
We know that the string order of a spin chain is defined as
$$\mathcal{O}^\alpha=\lim_{i-j\to\infty}\left\langle S_i^\alpha\prod_{k=i+1}^{j-1}\exp(i\pi S_k^\alpha)\ S_j^\alpha \right\rangle$$
now ...
2
votes
0answers
40 views
Translation Holonomy
I'm trying to get a mental image of translation holonomy.
I start with rotational holonomy, which corresponds to intrinsic curvature. This is the quantitative failure of a continuous process of ...
0
votes
0answers
48 views
Classical statistical model based on group multiplication
For a (finite) group $G$, consider the following classical statistical model on a 2 dimensional lattice with oriented edges:
Each edge carries a classical degree of freedom that can take values in ...
0
votes
0answers
341 views
Transfer matrix of 1D Ising model
I'm sorry if this is trivial, I've been stuck on a definition in Yeomans, Statistical mechanics of phase transitions. In chapter five she describes the transfer matrix of the 1D Ising model with ...
2
votes
0answers
56 views
Can we have a spin glass in the one-dimensional Heisenberg hamiltonian with nearest neighbours only?
Consider the one dimensional Heisenberg Hamiltonian of the form
\begin{equation}
H = - \sum_{<i,j>} J_{ij} \mathbf{S}_i \cdot \mathbf{S}_j
\end{equation}
with nearest neighbour interactions. ...
1
vote
0answers
171 views
Transverse field Ising model with open boundary conditions
what is the energy dispersion of the transverse field Ising model looks like in the case of open boundary conditions?
In the case of periodic boundary, the energy takes the form of
and the ground ...
2
votes
1answer
93 views
Why is a spin network a spinfoam's boundary?
i read in Wikipedia that spinfoams boudaries are spin networks, but nothing is said about what is a boundary in this case.
i know that a spin foam is a spin network where other colours and ...
