Questions tagged [spin-models]
A mathematical model used in physics primarily to explain magnetism.
468 questions
1vote
0answers
45views
Hybridization versus renormalization
Context Consider a Hamiltonian like $$ H = \sum_k \epsilon_k a^\dagger_k a_k + \omega_0 b^\dagger b + \sum_k V^{(1)}_k(a^\dagger_k b + a_k b^\dagger ) + \sum_k V^{(2)}_k ( b^\dagger + b ) a^\dagger_k ...
0votes
0answers
23views
Energy function in Hopfield original paper
I was reading Hopfield original paper (PDF) on so-called Hopfield networks and I notice that he takes an approach where the states of the neurons are either $0$ (inactive) or $1$ (active), which is ...
- 314
1vote
0answers
151views
What is the simplest 2D spin-$\frac{1}{2}$ model with a $\mathbb{Z_2} \times \mathbb{Z_2} $ topological bulk?
The Toric code can be described as a $\mathbb{Z_2}$ topological bulk theory and has a very simple lattice Hamiltonian description. Is there a similarly simple Hamiltonian that represents an exactly ...
- 558
3votes
1answer
171views
Are there interacting spin models with chiral symmetry?
A Hamiltonian $H$ has chiral symmetry if there exists some operator $\Gamma$ s.t. $$\Gamma H \Gamma^{-1}=-H.$$ Consider the $XYZ$ model on a chain $$ H=\sum_i J_xX_{i+1}X_{i}+J_yY_{i+1}Y_{i}+ J_zZ_{i+...
- 4,828
5votes
1answer
98views
Origin of Degeneracy in the Eigenvalues of the XY Model for Odd System Sizes
The XY model has the Hamiltonian $$H = \sum^{L-1}_{n = 1} \left( J^{x}_{n} X_{n} X_{n+1} + J^{y}_{n} Y_{n} Y_{n+1} \right).$$ I have written a code to calculate the eigenvalues of this model and found ...
- 51
2votes
0answers
40views
How is a vison excitation in a resonating valence bond (RVB) state related to photon of gauge theories? [closed]
I am reading Prof. Sachdev's review on quantum phases of matter (link: https://arxiv.org/abs/1203.4565) and I am a bit confused about how the analogy between U(1) photon excitations in QED and vison (...
2votes
0answers
62views
Problems with Heisenberg Hamiltonian and Quantum Mechanics [closed]
I was studying Magnons utilizing Kittel's Solid State book, however, I got caught by this doubt: Kittel uses a semiclassical formalism based on Heisenberg's spin hamiltonian for simplicity: $\mathcal{...
- 21
2votes
0answers
42views
Correlation matrix of spin glass model
Consider a mean-field spin glass model (e.g., the Sherrington-Kirkpatrick model or the spherical spin glass): $$ H_J(\sigma)= -\frac{\beta}{\sqrt N} \sum_{i,j=1}^N J_{ij}\,\sigma_i\,\sigma_j - h \sum_{...
- 161
3votes
1answer
227views
Obtaining renormalized Hamiltonian for 1D Ising model using renormalization group
In John Cardy's text Scaling and Renormalization in Statistical Physics, the 1D zero field Ising model $$\beta H:=-K\sum_i s_i s_{i+1}$$ is analyzed by grouping spins into blocks of three spins The ...
- 3,926
0votes
0answers
63views
Wilsonian renormalization group approach to the 2D Ising model with zero external magnetic field: search for the critical fixed point
I’m a beginner in the Wilsonian Renormalization (semi)Group approach and I’m trying to understand certain aspects. To express my doubts, I need to refer to the model I have in mind (Ising model). ...
1vote
0answers
40views
Derive expression for magnetic moment of a 1d magnet
Consider the simplest 1-dimensional magnet given by a chain of 1/2 spins where only neighbors interact. The general form of such magnetic Hamiltonian is given by: $$ \hat H = \Sigma_{i= -\infty}^\...
- 13
1vote
0answers
21views
Critical Behaviour of transverse variance
When dealing with phase transitions, the behavior of physical quantities can be described by the theory of critical exponents. For example, let's consider a one-dimensional spin $1/2$ $XY$ Hamiltonian ...
1vote
0answers
27views
Kitaev interaction and the exchange tensor
I am currently trying to understand how to model the intralayer magnetic exchange tensor in NiI$_2$. The relevant terms for this purpose have a contribution to the configurational energy as follows $\...
- 11
0votes
2answers
106views
Ground state of $S=1/2$ antiferromagnetic nearest neighbor Heisenberg chain
I can't find anything about this really. There are plenty of posts and papers clarifying matters about long range exchange interactions, the ferromagnetic case and $S>1/2$. Also I can find sources, ...
- 51
3votes
1answer
114views
Self-duality of 1D transverse field Ising model and ground state degeneracy
See THE review by Kogut for background. The quantum TFIM on a 1D chain has the Hamiltonian $$ H_{\text{TFIM}} \equiv - \sum_{i} \sigma_x(i) - \lambda \sum_i \sigma_z(i)\sigma_z(i+1) \tag{4.14} $$ ...
- 785
