Questions tagged [spin-models]
A mathematical model used in physics primarily to explain magnetism.
479 questions
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Source recommendation for spin glasses and their relation with SYK model
I want to learn Edwards-Anderson and Sherrington-Kirkpatrick models properly with their calculations (Replica symmetry, phase transition, etc.). I need couple of sources such as books and papers ...
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Eigenvalues of integrable Floquet system
Consider Kicked field Ising model Hamiltonian given as follows. (I am following the this paper, relevant calculations are in appendix A.)
$$
H_I=2 J \sum_k\left[\cos k\left(\hat{b}_k^{\dagger} \hat{b}...
- 163
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Phase transition for first moments in the 2D random-bond Ising model
I have a very basic confusion about the 2D random-bond Ising model on a square lattice with Boltzmann weight
$$\omega(J_{ij},\sigma_j)=\prod_{ij}(1-p)^{\delta_{J_{ij}=1}} p^{\delta_{J_{ij}=-1}} e^{-\...
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What is the mechanism behind the Curie point in ferromagnets?
I just finished up a uni course on magnetism, which mostly made sense, but I've been left with some questions about ferromagnetic behaviour; in particular, I'm not satisfied with my lecturer's ...
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Breaking of time reversal symmetry (TRS) and emergent magnetic field
Let us start with the Heisenberg Hamiltonian with nearest neighbour interactions,
$$H = \sum_{<ij>}S_i \cdot S_j$$ which perseveres time reversal symmetry.
In the presence of an external ...
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Available simulation tools for quantum Hamiltonians [closed]
I have a quantum Hamiltonian describing the interaction of several spins. I wanted to try to simulate my system and measure quantities such as the polarization of the spins, the magnetization and ...
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What is the spin-glass analogue of random LinSAT over $\mathbb{F}_p$?
Boolean variables $\vec{x} \in \{0,1\}^n$ can be mapped to Ising spins
$\vec{z} \in \{-1,+1\}^n$ via the relation $z_i = (-1)^{x_i}$. Under this mapping, a sparse XORSAT clause such as
$$
x_1 \oplus ...
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Integrability breaking due to bulk impurity
I was going through the paper on the effect of placing a bulk or edge impurity in the XXZ-Heisenberg model : here. Even though I can reproduce all the calculations and verify one of the main results i....
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Spin inhomoegenity vs optical inhomogeneity
I am studying the dependence of spin inhomogeneous linewidth across optical inhomogeneity in a rare-earth doped crystal. I notice some trends, but I couldn't find any similar studies anywhere.
Does ...
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$x$-$y$ symmetry breaking in dimer model
Suppose I have a fully packed hardcore dimer config on the square lattice with periodic boundary conditions in both directions.
The square lattice is bipartite and can be divided into $A$ and $B$ ...
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Path integral for a run-and-tumble particle
I am familiar with the path integral formalism for stochastic differential equations of the form (in 1d for simplicity)
\begin{equation}
\dot{x}(t) = f(x(t)) + \sqrt{2 D} \ \xi(t).
\end{equation}
It ...
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How to grow a quasi-1D chain in iDMRG?
In order to grow a 1D chain with nearest neighbour interaction for iDMRG in the language of Matrix Product State and Matrix Product Operator, I followed this note :
https://www.lassp.cornell.edu/erich-...
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Hybridization versus renormalization
Context
Consider a Hamiltonian like
$$
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 ...
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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 ...
- 364
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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 ...
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