# 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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### Universality and continuous variation of critical exponent close to a tricritical point

A tricritical point is a point at which a second order transition line and a first order transition line merge. At equilibrium, this point can be described by a landau potential (see for example this ...
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### Gaussian fluctuations reducing $T_c$ in Goldenfeld chapter 6

I am trying to understand generally how the critical temperature is shifted relative to its mean-field predictions even in dimensions greater than the critical dimension. This question is related to ...
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### Mean-field self-consistency and thermodynamic limit

Is the mean-field self-consistent-equation approach used to study, e.g., the magnetization of an Ising model able to take into account finite-size effects, or is it written, so to say, directly in the ...
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### Constant in mean-field Hamiltonian

When one obtains the mean-field Hamiltonian of a (classical or quantum) spin system and then needs to find the mean-field parameters by minimizing the expectation value of the Hamiltonian, does one ...
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### Heat Capacity in Mean Field Theory

I have been very confused with calculating the heat capacity when dealing with a Mean Field Hamiltonian. The Hamiltonian I am working with describes a spin lattice of fermions in 2D. I only count the ...
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### How is Weiss mean field approximation actually maximising the partition function of Boltzmann's distribution?

Considering other mean field approximation (e.g. Max entropy approach or $<S_i> = m_i +\delta S_i$ , $\delta S_i \simeq0$), a common approach that I've seen is that of maximising the partition ...
1 vote
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### Non-Saturation in Interacting Bose Gas Integral

I am independently working through some problems on Bose-Einstein condensation. In particular, I am trying to show that—in the Hartree-Fock mean-field approximation—for a Bose gas with contact ...
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### Tricky Integral: Evaluating Renormalized Ultraviolet "Divergent" Integral

I am trying to rederive the results presented in the paper, in particular equation (30). That is, I am trying to compute the correction to the ground-state energy of a dipolar condensate due to beyond-...
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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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### Is that a phase transition?

Let's consider a network of interacting dynamical systems comprising 2 populations (A and B) where the mean field description of the dynamics of the 2 populations is captured by the following ...
1 vote
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### Green's function for Anderson impurity model?

In this article "PHYSICAL REVIEW B 90, 155136 (2014) " (or here): Title: "Machine learning for many-body physics: The case of the Anderson impurity ...
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### Integral in mean field theory

Using MFT, I have obtained energy spectrum of a model to be: $$\mathcal{E}_k (m_0,\tilde m_e)=\sqrt{{(J_b \cdot m_o + J_a \cdot m_e)^2 + \frac{{J_p^2}}{{16}} \cdot \cos^2(k)}}$$ Now, in order to ...
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### How can I get the angle of the order parameter [closed]

I read a paper(PRL 100, 156401 (2008)), I want to try to draw picture 2 by myself. But I don't konw how to get the $\bar\phi$ and $\phi$.The honeycomb lattice is bipartite, consisting of two ...
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### 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, $E$, ...
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### 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 ...
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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 ...
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### 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, ...
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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 ...
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### Mean field theory of an Ising antiferromagnet

I am calculating the free energy of an Ising antiferromagnet under the static magnetic field, and trying to get an expansion of free energy near the Neel temperature. But my calculation leads to a ...
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