Questions tagged [spin-models]

A mathematical model used in physics primarily to explain magnetism.

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Bogoliubov-Valatin transformation generalisation

Considering the following Heisenberg Hamiltonian (with spin $S$ , and $J<0$ for the case of an antiferromagnet) when we only consider interactions between first neighbors in a square lattice in the ...
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How is concept of Lorentz local field considered in Heisenberg model?

The quantum Hamiltonian of Heisenberg model is usually given in the form: $$\textit{H}_{heisenberg}=-\sum_{i,j}J_{ij}\vec{S}_{i}\cdot\vec{S}_{j}-g\mu_{B}\vec{H}\cdot\sum_{i}\vec{S}_{i}$$ such that ...
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What exactly is the magnetic field $H$ at Heisenberg model?

The quantum hamiltonian of Heisenberg model is usually given in the form: $$\textit{H}_{heisenberg}=-\sum_{i,j}J_{ij}\vec{S}_{i}\cdot\vec{S}_{j}-g\mu_{B}\vec{H}\cdot\sum_{i}\vec{S}_{i}$$ such that ...
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Understanding inelastic neutron scattering intensities

Inelastic neutron scattering (INS) is commonly used to probe the magnetic structure of materials and to probe magnetic excitations (magnons) in a system. Unpolarized INS measures the spin-spin ...
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Bragg-Williams microcanonical esemble

In this question Bragg-Williams theory of phase transition of the forum someone was asking for Bragg-Williams aprox. and how to calculate entropy. The answer is clear and correct, the Bragg-Williams ...
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Conceptually understanding an Ising-type transition

I am currently reading the following paper. The system consists of a chain of mesoscopic superconducting islands (aka a Josephson Junction array), but each island also contains a quantum wire that ...
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The importance of upper critical dimension in spin glass models

In spin glass models the upper critical dimension is known to be 6, but recently it was discovered to be 8. What is the importance of upper critical dimension for spin glass models? We don't live in 6 ...
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Polaron transformation in quantum optics

I'm trying to understand the so-called polaron transformation as frequently encountered in quantum optics. Take the following paper as example: "Quantum dot cavity-QED in the presence of strong ...
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How to take into account finite temperature in transverse Ising chain?

A similar question has already been asked here What I'm wondering is how to take into account finite temperature in the transverse Ising chain and see how that affects the magnetization. The reason ...
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Reference request: Kawasaki dynamics for Ising model

I want to learn more about Glauber and Kawasaki dynamics which, by my understanding, are used to model lattice spin systems for the pre-equilibrium Ising model. There seems to be quite a few ...
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(In)finite lattice in quantum statistical mechanics: validity of phase classifications and TQFT [closed]

I would like to understand the motivation for studying quantum statistical mechanics, such as spin models, on an infinite lattice, or in other word, in the operator algebraic framework. I learned that ...
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Coding of Correlation function in spin chain

I have to code a correlation function for Spinoperators $S_x^i S_x^j$, $S_y^i S_y^j$ and $S_z^i S_z^j$ (basically $\vec{S}_i \vec{S}_j$) for two spins on two different sites of a spin chain. Can ...
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How do boundary conditions change during a spin transformation?

I am currently reading the following review paper: (1) Two Dimensional Model as a Soluble Problem for Many Fermions by Schultz et. al. Equation (3.2), which is reproduced below, introduces the Jordan-...
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Free energy calculation for spin glass with non-random interactions

In the Sherrington–Kirkpatrick model, $$H = \sum_{i,j} J_{ij} {s}_i {s}_j,$$ where $J_{ij}$'s are independent and identically distributed random variables, and in this case, the free energy may be ...
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Frustrated classical field theory

The frustrated Ising model (see e.g. this answer) is an example of a system that shows no unique ground state and many metastable states (its "energy landscape" is extremely complex). ...
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Interaction term in the Hamiltonian of transverse-field Ising model

I got a question about quantum transverse-field Ising model. The Hamiltonian has two terms which are external field term and interaction term. Why are there only $Z$-$Z$ interactions between ...
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Fourier Transform of Spin operators

Fourier Transform is often used to diagonalize an infinte or periodic lattice Hamiltonian, for example in the tight-binding model $$ \begin{aligned}H=t\sum_{\langle i,j\rangle}c_{i}^{\dagger}c_{j}\end{...
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How can I find the critical dimension for the Blum-Capel model near the tricritical point in mean field theory?

I believe that I have found the critical dimension for the critical temperatures on the critical line (that is, where the second order phase transition occurs), which is $D=4$. This is because the ...
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Spin hamiltonian matrix representation

To preface, I'm an applied mathematician trying to parse the meaning of physics notation I've come across in a paper. My goal is to understand the setting in terms of matrices and vectors so that I ...
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At the critical point, is Kramers-Wannier duality a unitary symmetry of the model?

I have in mind the transverse ising model and its (self-dual) generalizations, such as $$H_{TI} = \sum_i \sigma^z_{i}\sigma^z_{i+1} + h \sigma^x_{i}$$ and $$H_{SDANNI} = \sum_i (\sigma^z_{i}\sigma^z_{...
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Energy current in a quantum chain

I have seen in (e.g. this paper) the definition of the energy current in a chain with $H = \sum_{j=1}^L h_j$ where $H_j$ has support on the $k$ sites $j,j+1,j+2,...,j+(k-1)$ as $$J_j - J_{j+1} = i[H, ...
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Two lines of critical points described by CFTs with different central charges intersect. What happens?

There is a lovely set of two-parameter spin chains that can be mapped to quadratic fermions and studied quite exactly: $$H = -\sum_{i} \frac{1+\gamma}{2}\sigma^x_i\sigma^x_{i+1}+\frac{1-\gamma}{2}\...
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Why the entropy of non-zero nuclear spin is zero at $T = 0$?

When reading Concepts in Thermal Physics (second edition) by Stephen and Katherine about the concepts of the third law, I met with such a problem. The text reads as follows: Consider a perfect ...
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Log-law entanglement with large central charge contradict bounds on the entanglement entropy

I am trying to learn more about entanglement entropy in large but finite-size systems at critical points. I am still relatively new to conformal field theory, so it is not unlikely I have ...
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Connection between superfluid density and spin stiffness

I am currently trying to understand the apparent equivalence between spin stiffness and superfluid density. I (think I) understand how the XXZ model maps onto the Boson-Hubbard model with the ...
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If a spin $\frac{1}{2}$ particle flips its sign after a 360° rotation, why don't theorists just say it rotated by 180°?

Usually, when a wave or wave-like object or system goes through a $180^{\circ}$ twist or turn or whatever, we say it is opposite to how it was oriented before, and if it came across its former self ...
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Jordan-Wigner Transformations on fermionic system

I've been trying to use Jordan-Wigner Transformations on a given fermionic Hamiltonian. The given Hamiltonian is: $$ \hat{H}= -\sum_{m=1}^{N}(J_z \hat{S}_{m}^{z} \hat{S}_{m+1}^{z} + \frac{J_{\perp}}{2}...
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Traveling salesman problem and the Ising Hamiltonian

If one looks at the 2014 paper by Lucas (https://doi.org/10.3389/fphy.2014.00005) on "Ising formulations of many NP problems", he introduces multiple solutions to a variety of NP Complete ...
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Is the phenomenon of geometrical frustration in condensed matter physics related to some kind of topological invariant?

Edit (attempt to clarify my question a little bit): I’m not thinking geometrical frustration should be necessarily associated to a topological invariant in a direct way, but maybe local geometrical ...
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Why Can Electrons be Modelled as Classical Spins?

Although electrons are spin $1/2$ particles described by the Pauli matrices, the Ising model treats electrons as classical spins. As a result, the Ising model does not describe anything physical, but ...
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Absence of Symmetry Breaking in 1D Ising Model--Continuum Version

I have seen arguments for why there is no symmetry breaking in the 1D Ising model--for example, using the transfer matrix method to explicitly solve the model, and another of energy-entropy arguments ...
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$C$, $P$, $T$ symmetry of $O(3)$ non-linear sigma model

Consider the $O(3)$ nonlinear sigma model with topological theta term in 1+1 D: $$\mathcal{L}=|d\textbf{n}|^{2}+\frac{i\theta}{8\pi}\textbf{n}\cdot(d\textbf{n}\times d\textbf{n}).$$ The time reversal ...
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Transfer matrix for 1D $XY$ model in zero external field

In zero external magnetic field, and with periodic boundary conditions, the XY-model on a 1D crystal lattice can be expressed by the Hamiltonian: $$ \mathcal H=-J\sum_{i=1}^N\vec S_i\cdot\vec S_{i+1} ...
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Matrix element and Dirac notation

If $$ T= \left[ \begin{array}{cccc} e^{\beta J} & e^{-\beta J} \\ e^{-\beta J} & e^{\beta J} \\ \end{array} \right] $$ and $$Z = \sum_{S_i=\pm 1} ... \sum_{S_N=\pm 1} \exp{\beta J(\vec{...
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Can a classical approximation of a quantum model give smaller energy?

I'm analyzing phase transitions of the XXZ model on a honeycomb lattice. The fully quantum Hamiltonian can be written as follows $$ H = - \bigg( J \sum_{<i, i'>, i<i'} \bar{S}_i \cdot \bar{S}...
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Spin Glass Hamiltonian

Why do Edwards and Anderson use the hamiltonian $$ H = \sum_{i,j} J_{ij} \mathbf{s}_i \cdot \mathbf{s}_j $$ to describe the interactions in a spin glass? Naively I would think that from the ...
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How has Parisi's nobel-prize winning work been applied to all kinds of complex systems?

As discussed briefly in this APS Physics editorial, Nobel Prize: Complexity, from Atoms to Atmospheres, the most important works of the recent Nobel prize winning physicist concern the study of the ...
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How local are the conserved charges in a quantum integrable model?

For the purposes of this question, let us define a quantum integrable model as one solvable by the Bethe Ansatz. That structure endows the model with a set of conserved charges $\{H^{(n)}\}$ whose ...
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What is the difference between a skyrmion and a magnetic vortex?

Skyrmions and magnetic vortices are spin structures occurring in magnets. What are the differences between them? More specifically, I would like to understand their origin and how to distinguish them.
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Ground state magnetization at T=0

For a given Hamiltonian with spin interaction, say Heisenberg Model $$H=-J\sum_{i,j} s_i s_j- B\sum_{i} s^z_i$$ Magnetization $M(B) = \sum_i s^z_i$, at any field $B$ can be obtained by taking emsemble ...
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Bi-reflection of spin waves

When an external magnetic field is exerted on one side, the spin wave reflects in two directions. Why does this happen?
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Why can we choose spin-1/2 degrees of freedom to commute?

Edit 2: The previous title of this question was "Why are qubits bosonic?" Thanks to the answers that have been provided so far, I now realize I asked my question in a sloppy way. The ...
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Hamiltonian density of a spin Hamiltonian

A many-body Hamiltonian in second quantization is written as $$ H = \int d\vec r \Psi^\dagger_{\vec r} H_1 (r) \Psi_{\vec r} $$ where $H_1(r)$ is one-body Hamiltonian. For example, for a non-...
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Excitations and gauge symmetries of the classical 2d s=1/2 Néel phase

Consider a 2d square lattice consisting of localized spin-1/2 Ising moments with uniaxial anisotropy $D$, conferring a classical Néel state below a paramagnetic phase boundary $T_{\mathrm{N}}$. In ...
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How is two-level optical transition in a spin 1 system affected by the third level?

Suppose you have a spin-1 system. Let us resonantly drive the transition between any 2 levels (say 0 1 transition). How would the the presence of the third level (-1) state affect this transition? We ...
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Why is long-range coherence necessary for an incompressible liquid?

I am trying to understand this line: The chiral spin order parameter captures some, but not all, of the properties we would like to postulate of a quantum spin liquid. It has the desirable feature of ...
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Conserved charge in Density Matrix Renormalization Group(DMRG)

Currently I am facing a problem which relates to the conserved quantities in DMRG. I use old-fashioned DMRG (Steven White approach) to compute the ground state of certain models. However, the ground ...
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What is helical Dirac nature?

A concept in Spintronics which can not be found on Wikipedia. The picture is from a review of Spintronics of 2016 by Fert.
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Why and how exactly do spinning electrons create a magnetic field?

I have just been told that if you had a spinning electron completely isolated, even that one electron would have a magnetic north and south pole. I have also been told that all metals have spinning ...
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Minor details of Mermin-Wagner

In the proof of Mermin-Wagner (e.g., scholarpedia), there is a minor assumption that the average magnetization $m_\Lambda (h)$ converges in the thermodynamic limit $\Lambda \to \mathbb{Z}^d$ to some $...
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