# 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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### Obtain Mean Field Equations for Spin Models using a uniform Ansatz

I would like to see how my model I am working on behaves in the limit of infinite dimensions so I get a little bit of intuition for the low dimensional case. In the paper I am reading they have a ...
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### Derivation of non-linear Schrödinger equation from many-body QM

I hope this (and not MathOverflow) is the right place to post this question. I am a math student taking a methods of mathematical physics course, in which we cover the solution theory the non-linear ...
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### In general, do critical points of continuous phase transitions have $\beta =0$?

Consider a phenomenological modelling of a continuous phase transition, where the Lagrangian of the system is given by $$L=\frac{a}{2}\phi^2+\frac{\lambda}{4}\phi^4-h\phi.$$ Here $\phi$ is the order ...
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### Can third-order phase transitions be understood from a symmetry-breaking viewpoint? [duplicate]

First-order phase transitions like solid-fluid can be understood as breaking of translational symmetry into lattice symmetry (also rotations into discrete rotations). The characteristic of these ...
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### Non-renormalizable theory and mean field theory

For $\phi^4$ theory, when $d>4$, the theory becomes nonrenormalizable, but when $d>4$, we can use mean field theory to calculate the exact critical exponents. The intuition behind mean field ...
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### Bogoliubov transformation BCS Hamiltonian

I am reading on the BCS theory and the bogoliubov transformation to diagonilize the BCS Hamiltonian. And there is one step that I really can't seem to get. So the Hamiltonian looks like this: \begin{...
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### In mean-field theory, why are the collisions of particles in the mean-field neglected?

Mean field theory is a tractable framework for analyzing parameters of a continuum or an infinite number of identical micro-particles or agents. The former has been treated extensively in statistical ...
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### Question regarding the derivation of equation for anomalous density

I was reading this paper and have a question regarding the derivation of equation $3.7$ for $\tilde m$ from equation $3.4c$. In particular, I was having trouble seeing why \begin{align} (h^\text{sp}(\...
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### How to find the functional self-energy?

I have a system with $e$-$e$ interaction. After using the mean field approximation, my Hamiltonian has the following form: $H = H_0 + H_I$, which $H_0$ is the non-interacting and $H_I$ is the ...
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### Iterative Greens function calculation

I have a Hamiltonian which has an interactive and non-interactive parts. $H = H_0 + H_I$ $H_I$ comes from the non-local electron-electron interaction and must be calculated self-consistently. I ...
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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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