Questions tagged [mean-field-theory]
The study of systems of many interacting components by replacing the actual interaction between the components with an effective "averaged" one.
123 questions
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Mean field theory Vs Gaussian Approximation?
I am getting confused about the distinction between Mean-field theory (MFT) and the Gaussian approximation (GA). I have being told on a number of occasions (in the context of the Ising model) that the ...
17votes
4answers
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Validity of mean-field approximation
In mean-field approximation we replace the interaction term of the Hamiltonian by a term, which is quadratic in creation and annihilation operators. For example, in the case of the BCS theory, where $...
user82905
17votes
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Mean-field theory : variational approach versus self-consistency
I have a general question concerning mean-field approaches applied to quantum or classical statistical mechanics. Does determining the mean-field by a variational approach always imply that the self-...
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Why is Hartree-Fock considered a mean-field approach?
In studying the Hartree-Fock method for solving systems of interacting particles, I have often found that the method is referred to as a mean-field approach. Wikipedia's page for instance says that ...
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Why does Josephson's identity $d\nu=2-\alpha$ only hold for mean field theory in dimension $4$?
For phase transition, when approaching the critical point, the heat capacity $C \propto \tau^{-\alpha}$ and correlation length $\xi\propto \tau^{-\nu}$, with $\tau := \frac{T-T_\mathrm{c}}{T_\mathrm{c}...
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1answer
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Mean-field theory and spatial correlations in statistical physics
In statistical physics, mean-field theory (MFT) is often introduced by working out the Ising model and it's properties. From a spin model point of view, the mean-field approximation is given by ...
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9votes
2answers
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Lagrange multiplier in spin liquid mean-field theory (Paper by X.G. Wen)
My question is about a step in this paper: PhysRevB.65.165113 (X.G. Wen) page 6 Or alternatively: PhysRevB.90.174417 page 3. All the papers concerning spin liquids and the projective symmetry group ...
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1answer
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Mean-field theory in 1D Ising model
A mean-field theory approach to the Ising-model gives a critical temperature $k_B T_C = q J$, where $q$ is the number of nearest neighbours and $J$ is the interaction in the Ising Hamiltonian. Setting ...
9votes
3answers
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Is density functional theory a mean-field theory?
Is density functional theory exact or just a mean-field theory?
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1answer
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Are there good resources explaining mean field approximation?
I am a computer science master student. In a statistical learning theory course I am taking, mean field approximation was introduced to approximately solve non-factorizable Gibbs distributions that ...
8votes
1answer
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Is Hartree-Fock a standard mean field approximation?
I have read many times that Hartree-Fock is a mean field approximation, but I struggle to reconcile it with a standard mean field approach. In the simplest form of mean field approximation, we utilize ...
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1answer
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Excitation spectrum in BCS theory and mean field theory
I've recently been learning about the BCS theory of superconductivity. An extremely rough idea is as follows: given the interacting BCS Hamiltonian $$ H = \sum_{\vec{k}\sigma} \xi_{\vec{k}} c^{\dagger}...
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1answer
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The "Hartree-Fock energy" in the Feynman formalism vs the Hartree-Fock method
This question has been previously asked, but I do not understand the answer. When calculating the ground state energy of an interacting system by a perturbative expansion in terms of Feynman diagrams,...
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1answer
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Magnetization in Quantum Transverse Ising Model: Mean Field Theory vs Reality
One of the canonical examples of mean field theory concerns the ground state ($T=0$) of the transverse field Ising model, with Hamiltonian $$H = -J\sum_{<ij>} \sigma^z_i \sigma^z_j-h \sum_i\...
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7votes
1answer
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How to judge constitution boson "BEC" from the dispersion of bosonic quasi-particle?
We know the spin-1/2 anti-ferromagneitc (AFM) Heisenberg model can be expressed as Schwinger boson $$\begin{array}{l}{S_{i}^{+}=b_{i \uparrow}^{\dagger} b_{i \downarrow}} \\ {S_{i}^{-}=b_{i \downarrow}...
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