Questions tagged [spin-models]

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8
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144 views

Do bipartite spin glasses have simple relaxation dynamics?

From what I gather, a Boltzmann machine (BM) is essentially a spin glass with no applied field evolving under Glauber dynamics (if this is at all mistaken, I don't think it will be off enough to ...
5
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58 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, ...
4
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154 views

Kosterlitz-Thouless in the XXZ chain: instanton condensation?

The anisotropic spin-$\frac{1}{2}$ Heisenberg chain $$H = \sum_n S^x_n S^x_{n+1} + S^y_n S^y_{n+1} + \Delta S^z_n S^z_{n+1}$$ is known to have the same physics as the two-dimensional classical XY ...
3
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1answer
44 views

Weyssenhoff fluid and Frenkel condition

A Weyssenhoff fluid is a continuos fluid with spin. The spin is described by an antisimmetric tensor $s{_{ab}}=s{_{[ab]}}$ satisfying the Frenkel condition \begin{equation} s{_{ab}}u{^b}=0 \end{...
3
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0answers
72 views

Product of Local Hamiltonians is Local

Let $H_1,H_2$ be local Hamiltonians (i.e. interactions are finite range). Let us form the product of the exponentials of both. By Baker-Campbell-Hausdorff, this defines a third Hamiltonian, $$e^{H_1}...
3
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350 views

What is the relation between the Holstein-Primakoff Transformation and Bethe's Ansatz for the Heisenberg Ferromagnet?

Bethe's Ansatz is a method to find the eigenenergies and eigenstates of the Heisenberg ferromagnet (see also spin waves). For a general n-excitation state it involves solving rather complicated ...
3
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0answers
191 views

Toric Code and the String-Net Model

What, exactly, makes the toric code a quantum error-correcting code as opposed to any other string-net model? What makes it special? The way I understand it, it's a normal string-net model on a torus, ...
2
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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)....
2
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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
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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 ...
2
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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. ...
2
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46 views

Force caused by the magnetic field on the electron spin

I have read there are two ways to express the force caused by a variable magnetic field over a magnetic moment depending on the source of the magnetic moment since it can come from a dipole or a loop ...
2
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0answers
64 views

Correlation functions of exactly solvable 1D quantum models

Quantum 1d spin-1/2 transverse Ising and XY models are both related to 2d classical Ising model. Are there any known simple explicit relations between correlation functions of this models? Something ...
2
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1answer
86 views

Mean Field Theory on Random Graphs

We traditionally use mean field theory to analyze graphs with some degree of translation invariance. This assumption of translation invariance enables a key algebraic simplification which makes ...
2
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0answers
274 views

Exact solution of the Hubbard model in one-dimension

Does anyone know a full and well-explained account on how to solve the one-dimensional Hubbard model? I understand that the first solution is given here, but it's a little bit involved. Perhaps just ...
2
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197 views

Transfer Matrix formalism

I am trying to apply the transfer matrix formalism to an Ising model problem, and am having some difficulties deriving the correct matrix to use. The problem is as follows. There is an infinite chain ...
2
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105 views

The Ising approximation - what exactly is it?

I am slightly confused about the nature of the Ising model to study ferromagnetism. Consider the Heisenberg Hamiltonian with Zeeman term: \[H=-\frac{1}{2} \sum_{i\ne j}J_{ij} S_i\cdot S_j+g\mu_B {B}\...
2
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223 views

Difference between 1D and 3D Heisenberg model

As is given in Wikipedia the $1$D Heisenberg model is: $$ \hat{H} = -J\sum_{i=1}^N \sigma_i\sigma_{i+1} - h\sum_{i=1}^N \sigma_i $$ And the $3$D Heisenberg model is: $$ \hat{H} = -\tfrac{1}{2} \...
2
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0answers
231 views

Potts Model: the critical temperature from a free energy - in general

In describing the Three-State potts model with mean field theory, I've arrived at the following Helmholtz free energy for my system: $$ F = \frac{1}{2} J N z m^{2} - N k T \mathrm{ln}\left( \exp\left[ ...
2
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40 views

Example of spin chains with finite-lifetime quasi-particles?

Does anyone know a one-dimensional spin model where the low-energy excitations have a finite lifetime? (E.g. in terms of the spectral function $\mathcal S(k, \omega)$ this means one would get a finite ...
2
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1answer
116 views

Spin networks - resources

I am very interested in studying spin networks. Where can I begin? I want to understand them at their basic level. Which reference is good to get more technical details?
2
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197 views

The ground state of AFM Heisenberg model $H=+J\displaystyle \sum_{\langle i,j\rangle} \vec{S}_i \cdot \vec{S}_j$ on the triangular lattice?

What is the order -- the ground state of AFM Heisenberg model $H=+J\displaystyle \sum_{\langle i,j\rangle}\vec{S}_i \cdot \vec{S}_j$ on the triangular lattice, with $J>0$ and nearest neighbor ...
2
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0answers
135 views

Chiral spin liquid flux states on the Kagome lattice

Short version: Is it possible to arrange the fluxes for the Kagomé lattice with triangle flux $\phi_\triangle=\frac{\pi}2$ and hexagon flux $\phi_{hex}=0$ using a single unit cell? Longer version: I ...
2
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0answers
270 views

Ising model at high vs. low temperature

The output of the Ising model over a 2D binary lattice looks to have spin states uniformly distributed over the lattice for high values of the temperature parameter with the output attaining ...
2
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0answers
344 views

Fermion 1D Hubbard Model ground state in the U = 0 limit

I am trying to determine the ground state of the 1D fermionic Hubbard model at half-filling of $2L$ sites with $L$ electrons with spin-$\uparrow$ and $L$ electrons with spin-$\downarrow$ in the $U=0$ ...
2
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1answer
117 views

Lattice Gauge and Spin Network

I see the similarity between the Lattice Gauge and Spin Network. (For example, the both theories depict the node part as quantum (the latter is explained as spin).) Are there any other mathematical, ...
2
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0answers
81 views

Spin Transition Energies

I am reading a paper: http://arxiv.org/ftp/arxiv/papers/1305/1305.2445.pdf On p. 22, the following Hamiltonian is given: $$ H = \mu_B g \mathbf{B} \cdot \mathbf{S} + D(S_Z^2+\frac{1}{3}S(S+1)) + E(...
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18 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. ...
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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
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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=...
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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 ...
1
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0answers
23 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....
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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 ...
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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 ...
1
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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
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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+...
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0answers
27 views

$p$-spin spherical spin glass

Consider the $p$-spin spherical spin glass model with Hamiltonian $$H_{N,p}(\sigma)=\frac{1}{{N}^{\frac{(p-1)}{2}}} \sum \limits_{i_1,...i_p} J_{i_1,...i_p} \sigma_{i_1} \sigma_{i_2} .. \sigma_{i_p} $$...
1
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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 ...
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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
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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 ...
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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 ...
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0answers
173 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 ...
1
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1answer
70 views

Acoustic, optical, ferromagnetic and antiferromagnetic spin-waves?

In the context of spin-waves I have seen the following words as descriptors*: Acoustic Optical Ferromagnetic Antiferromagnetic which I have seen used together e.g. "acoustic ferromagnetic spin ...
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0answers
85 views

Correlation between spins using delta function in Potts model

In reading about the Potts model, I found this correlation: $$\langle s_{i}s_{j} \rangle = \frac{q}{q-1}\frac{1}{N_{p}} \sum_{s_{i},s_{j}} (\delta(s_{i} - s_{j})-\frac{1}{q})$$ with the following text:...
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0answers
87 views

Boundary critical exponents of the 1D quantum XY model

Critical properties of the two-dimensional Ising model in the bulk and at the boundary are characterized by different critical exponent, see Ising model: exact results and McCoy: The boundary Ising ...
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0answers
76 views

Naive question about the physical dynamics for classical Ising model

Suppose we have a 2D Ising model in physical world, at finite temperature, the system have to obey the Boltzmann distribution: $$P(\{s_i\})=\frac{1}{Z}\exp^{-\beta E(\{s_i\})}$$ where $Z$ is the ...
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0answers
85 views

Spontaneously breaking $SO(3)$ symmetry without $\mathbb Z_2 \times \mathbb Z_2$?

Are there any examples of Hamiltonians (probably spin models) with an $SO(3)$ symmetry which is spontaneously broken down in the ground state without breaking the subgroup of $\pi$-rotations?
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186 views

How to measure spin-spin correlation in Heisenberg Model?

How to measure the spin-spin correlation in Heisenberg Model? I use the QMC method, working on 2d case.
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0answers
77 views

Validity of Ising model for mean field thoery

The Heisenberg model for the Hamiltonian of a ferromagnet is given by: $$H=-\frac{J}{2} \sum \vec{S}_i\cdot \vec{S}_j+\mu_B B \sum_i S^z_i$$ when performing mean field theory, to find $\chi$, we ...
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0answers
51 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 ...