# 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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### Calculating the average value at zero temperature (Coulomb Staircase)

As I was trying to understand slave rotor mean field theory (arXiv:cond-mat/0404334), I have faced a problem while solving the Coulomb staircase example in which I had to calculate the expectation ...
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1 vote
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### Maxima (or saddle points) of the free energy are thermodynamically stable phases?

In classical mechanics, the equations of motions are derived following the principle of stationary action, i.e., by taking the minima, maxima, or saddle points of the action $\delta S=0$. The ...
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### Detailed treatment of a liquid-gas phase transition in Landau Theory approach

I have been studying the Landau theory for critical second order phase transitions. I am looking for a specific and detailed treatment of a liquid-gas phase transition near the critical point. Many ...
223 views

### Does the Hartree Fock energy of a virtual orbital fulfill the virial theorem?

In calculating the ground state of atoms or molecules at the equilibrium geometry, the expectation values of the kinetic, $⟨T⟩$, and potential, $⟨V⟩$, energies relate to the total energy, $E$, ...
30 views

### How to select a proper term to proceed a mean-field approximation?

Recently I read some literature about how people use the mean-field approximation to solve a particular physical problem. However, I saw people using it in a different way when they dealt with ...
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### Mean field theory of classical system of charged particles in presence of external magnetic field

Suppose, there is a system of charged particles interacting via a pairwise additive potential and in the presence of a position dependent external potential and an external magnetic field. The ...
28 views

### Long Range interaction in Ising Model [duplicate]

How do we apply mean Field Approximation to the following Hamiltonian of Ising Model in 1D? \begin{equation} \mathcal{H} = -\sum_{i=1}^{N}\sum_{j<i}\frac{J}{\lvert i - j \rvert ^ {\alpha}}\sigma_i \...
1 vote
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### Chemical potential terms in Hamiltonian

In the derivation of grand canonical ensemble, which assumes that the physical system (with Hamiltonian $H$) has an average energy $E$ and an average number of particles $\bar{N}$, the density matrix ...
327 views

### Multi-channel mean field theory

I have always been confused about the theoretical foundation of the mean field approximation. Below I follow the book Many-body Quantum Theory in Condensed Matter Physics by Bruus and Flensberg, ...
1 vote
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### Energy gap of mean field model for transverse ising chain

Polynomials of spin operators with real coefficients appear not infrequently in Hamiltonians and in mean field theory, and there are often tricks to find their eigenvalues. For example, the polynomial ...