Questions tagged [spin-models]

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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, ...
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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. ...
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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 ...
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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 ...
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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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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 ...
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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 ...
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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}\...
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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 ...
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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 ...
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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....
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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 ...
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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?...
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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 ...
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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 ...
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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=...
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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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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 ...
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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 ...
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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 ...
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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)....
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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 ...
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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}\...
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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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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: ...
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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 ...
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27 views

$p$-spin spherical spin glass

Consider the $p$-spin spherical spin glass model with Hamiltonian $$H_{N,p}(\sigma)=\frac{1}{{N}^{\frac{(p-1)}{2}}} \sum \limits_{i_1,...i_p} J_{i_1,...i_p} \sigma_{i_1} \sigma_{i_2} .. \sigma_{i_p} $$...
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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?
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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?
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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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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+...
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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&...
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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\...
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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 ...
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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 ...
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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,...
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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 ...
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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 ...
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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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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 ...
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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 $\...
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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&\...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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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 ...