# 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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### 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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### 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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### 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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### 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 ...
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}\... 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 ... 0answers 40 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 ... 1answer 469 views ### Quenched systems - disorder average (SYK model) In a system with quenched disorder one is usually looking for self-averaging quantities, i.e., quantities such that the average over the couplings produces a typical" configuration in the ... 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 ... 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.... 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?... 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 $$H ... 1answer 127 views ### Why does a spinning nucleon generate a magnetic field? I am trying to understand how NMR works, but I am not sure why a spinning nucleon produces a magnetic field. Is this a consequence of the quark structure inside? 1answer 98 views ### Two spin-1 system and the projector onto total spin 2 subspace [closed] I am having trouble grasping the projection operators in the context of composite spins system, e.g. with two spin-1. First off, a projector P is said to be an operator that squares to itself, P^2=... 0answers 65 views ### Why the correlation function of 2D classical XY model is written so? 2D classical XY model$$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 ... 1answer 182 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 ... 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 ... 1answer 148 views ### Find out ground sates for large 2D classical spin model Reaching the ground state of a large 2D classical spin model (e.g. classical Heisenberg model) might be a relatively difficult task while using conventional "flip/reject" Monte Carlo method. The ... 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 ... 0answers 58 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 ... 0answers 78 views ### Can someone explain to me the Rokhsar-Kivelson Hamiltonian? [closed] The following paper shows the hamiltonian of the 2D quantum dimer gas (page 2) http://www-thphys.physics.ox.ac.uk/people/ClaudioCastelnovo/Talks/050209_MIT.pdf Here are some questions I have. Why ... 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 $$where S_i\in\{-1,1\}, and the summed pair i,j can be any two distinct indices (not necessary adjacent spins).... 1answer 89 views ### One-dimensional SU(3) Heisenberg Model, the non-linear sigma model, \theta-term Let's consider a one dimensional SU(N) antiferromagnetic Heisenberg Model with an irreducible representation and its conjugate on alternating sites, such that they correspond to a Young tableaux ... 1answer 84 views ### What is the order parameter of 2D generalized XY model? I'm now studying the phase transition of 2D generalized XY model. This model considered here has a mixture with ferromagnetic and nematic-like interactions,$$\mathcal{H}=-\sum_{\langle i j\rangle}\... 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: ... 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: $$H_1 = -t\sum_i \big(c_i^\dagger c_{i+... 0answers 20 views ### Exchange stiffness for HCP I am studying the exchange interaction, which can be described with the Heisenberg Hamiltonian: \hat{H} = -\sum_{i,j}J_{ij}\hat{\mathbf{S_i}}\cdot \hat{\mathbf{S_j}} In the framework of constant ... 0answers 27 views ### p-spin spherical spin glass Consider the p-spin spherical spin glass model with Hamiltonian$$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} $$... 0answers 41 views ### Which phenomenon is related to the spin of photons? [duplicate] The phenomenon of the deflection of a moving electron in a magnetic field is related to the electrons spin. From which phenomenon it is concluded, that photons have a spin? 1answer 37 views ### Constructing PEPS representation of an arbitrary quantum state Given a quantum state we can construct its MPS (Matrix Product State) representation by doing a series of singular value decompositions. Given the freedom to choose arbitrary bond dimensions the MPS ... 1answer 56 views ### Interaction in spin models In the Heisenberg Spin model, the spin components of spins in the same direction at different lattice sites couple together. Is there a physical scenario where, say, the x Spin component of a spin ... 1answer 143 views ### Relation between spin and polarization of photon? [duplicate] What is the possible spin configuration of photon? And does spin has any relation with polarization? 1answer 48 views ### A dreidel on a spinning table In the spirit of the holidays. Let's assume that a dreidel is spinning counter-clockwise at frequency f on a table. From external point of view, what will I see if I rotate the table clockwise at ... 1answer 62 views ### Average entropy of a subsystem In this paper by Don Page, https://arxiv.org/pdf/gr-qc/9305007.pdf, He conjectures average entropy of a substem of dimension m with Hilbert space dimension mn, m \leq n. to be : S_{mn} = \sum_{n+... 1answer 84 views ### Mean Field Theory on Random Graphs We traditionally use mean field theory to analyze graphs with some degree of translation invariance. This assumption of translation invariance enables a key algebraic simplification which makes ... 2answers 218 views ### Pauli matrices as measurement operators versus spin probability Pauli matrices tell us what the spin of a particle is along a certain axis. Let's say I want to measure the spin along the z-axis then the pauli operator$$\sigma_z = \begin{bmatrix}1&&0\\0&... 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 $$H = J\sum\... 2answers 154 views ### How can I say whether a Hamiltonian is integrable or not? The transverse field Ising Hamiltonian$$ H = J\sum_{i=0}^{N}\sigma_{i}^{z}\sigma_{i+1}^{z}+h_{x}\sum_{i=0}^{N}\sigma_{i}^{x} $$is integrable because it can be exactly solved using Jordan Wigner ... 1answer 136 views ### Integrability of generalized Richardson-Hubbard model Recently I got a bit interested in the possibility of finding spectrum of few interesting class of lattice quantum mechanical hamiltonians like Richardson's pairing hamiltonian, 1D Hubbard hamiltonian,... 0answers 26 views ### Discrepancy regarding Husimi Probability distribution calculation I am trying to simulate a system of j qubits and for visualization of the dynamics considering the Husimi distribution of the state. To carry out the projection onto coherent states I have proceeded ... 1answer 186 views ### Information from four point correlation functions in Ising model For a one-dimensional classical Ising model with the Hamiltonian$$H=-J \sum_{i}\sigma_{i} \, \sigma_{i+1}$$where \sigma=\left\{+1,-1\right\} one can calculate two point correlation for the spins$$... 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 ... 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 ... 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 ... 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$\...
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 ...