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Tagged with mean-field-theorythermodynamics
6 questions
0votes
0answers
140views
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 ...
1vote
3answers
237views
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 ...
- 3,593
2votes
1answer
701views
How is the van der Waals equation a mean-field model?
The van der Waals equation for real gases is $$\left( P+a\frac{n^{2}}{V^{2}}\right)\left( V-nb\right)=nRT$$ where $a$ and $b$ are constants, $n$ is the number of moles, $R$ is the gas constant, and $...
user27771
5votes
1answer
358views
Legendre Transformation of Landau Free Energy
I am trying to get an intuition for the Legendre Transformation of a generic Landau free energy, e.g. for the Ising model with magnetization $m$ given by $$F(m) = \frac{a}{2} m^2 + \frac{b}{4} m^4 + \...
- 758
1vote
1answer
395views
Landau free energy, ising mean field and the "full partition function". Discrepancy between two similar approaches
From what I understand, for example, in the neighbor interactions Ising model, we can write the partition function as: $$Z = \sum_{m}\Omega(m)e^{-\beta E(m)}=\sum_{m}e^{-\beta \tilde F(m)}=e^{-\beta F}...
- 2,175
2votes
2answers
225views
Product Rule for Partition Sums $Z_N=(Z_1)^N$
For the 1D Ising model with the Hamiltonian $$H=const.-\mu h' \sum_i S_i^z$$ we can write the canonical partition sum as $$Z_N = \sum_{ \{ S_i^z \}_N } e^{-\beta \mu h \sum_i S^z_i} = \sum_{ \{ S_i^...
- 485
