# 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.

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### Correlations in Ising mean-field theory

I am reading the book "Critical Dynamics - A Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior" (sections 1.1.2 and 1.1.3) and have been somewhat confused about the ...
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### Finite range 1D Ising model vs. infinite range Ising model

Ising model is defiend as $$\mathcal{H}=-H\sum_i S_i -\frac{1}{2}\sum_{i,j}J_{ij}S_i,S_j$$ In 1D we assume that indices $i,j$ are integers, $i,j\in\mathbb{Z}$, and that the coupling depends only on ...
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### Ising model 2D and mean field theory

Consider the 2D Ising model. Now, let's divide it into 4-spins blocks and treat the interaction inside each block exactly, while applying the mean-field approximation to the interaction between blocks....
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### Mean Field Theory for Lindblad Equations

I am working through the Appendix A.1 and A.2 of the paper Topology by Dissipation and try to learn something about the final result. The initial situation is a Lindblad-equation. Then one does a mean-...
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### Ambiguity of mean field approximation

I have a Condensed Matter Hamiltonian on some lattice (eg. square or triangular) \begin{equation} H = \sum_{i,j} :\hat{a}_j^\dagger \hat{a}_i \hat{a}_i^\dagger \hat{a}_j: = \sum_{i,j} \hat{a}_j^\...
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### How can I express a two body HFB hamiltonian in a quasi particle HFB base?

The problem is the flowing: Let $H$ be the standard two body Hamiltonian: $$H=\sum_{ab}t_{ab}c_{a}^{+}c_{b}+\frac{1}{4}\sum_{ab}v_{abcd}c_{a}^{+}c_{b}^{+}c_{c}c_{d}$$ Were {$c_{a}^{+}c_{a}$} is the ...
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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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### How to actually find a Hartree-Fock ground state?

I am interested in finding the Hartree-Fock ground state for a system of interacting fermions (with totally local scattering, so a delta-function interaction potential). I have read through some ...
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### Higgs Mechanism in Landau-Ginzburg approach

I'm experiencing some troubles with one of the exercises in Kardars book on Statical physics of fields (problem 5 Ch3) or see https://ocw.mit.edu/courses/physics/8-334-statistical-mechanics-ii-...
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### Mean-Field Theory in Second Quantization Formalism

Consider the Ising model in statistical physics $$H=-J\sum_{\left<i,j\right>}s_{i}s_{j}-\mu h\sum_{i}s_{i}$$ In this case mean-field approximation is done by replacing the surrounding spins ...
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