# 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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### The cavity method of Ising model in infinity dimension and dynamical mean field

In the article "Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions" chapter III.A, when discussing the cavity method of Ising model, the ...
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### Why do mean field theories neglect quantum correlations?

A measure of the quantumness of correlations is given by the quantum discord as introduced by Zurek in this paper for example. But I have also read in this paper, wherein they use mean field ...
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### Mean-field theory for a heterogeneous Ising model with two types of particles

Let's say I have an Ising model, but this time with two kinds of particles, A and B. Let the spin of particle A be denoted by $\sigma ^a$, and the spin of particle B by $\sigma ^b$. Let the total ...
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### Question about the so-called upper critical dimension

It is often said that above the upper critical dimension, the mean field theory is correct. What is the precise meaning of this statement? Let us be specific and consider the $d$-dimensional Ising ...
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### Correlation function calculation

From Mehran Kardar's Statistical Physics of Fields page 38 section 3.2 [...] $I_d(x,\xi)$ is the solution to the following differential equation $\nabla^2 I_d(x) = \delta^d(x)+ I_d(x)/\xi^2$ ...
From Statistical physics of fields by Mehran Kardar page 45 section 3.6 [...] the partition function including small fluctuations is \begin{align} Z \approx e^{-V\left(t/2 \cdot \overline m^2 +...