# Questions tagged [partition-function]

The partition function describes the statistical properties of a system in thermodynamic equilibrium, and is constructed to represent a particular statistical ensemble (microcanonical, macrocanonical, grand canonical).

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### What is the relation between the partition function from Stat. Mech. And the Path Integral? [duplicate]

Beside the fact that they look identical when you take imaginary time in the path integral formulation. I understand we doing statistics and we are just integrating over all states with a relative ...
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### Interpretation of probability in Statistical Mechanics

In statistical mechanics, in particular the canonical ensemble, the probability of the system to have a particular state is given by : $$P_i=\frac{e^{-\beta E}}{Z}$$ Here $Z$ is the partition function ...
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### Confusion regarding the use of partition function

Suppose we have a system filled with $N$ particles. There are $k$ energy levels in this system, labeled by $\epsilon_i$, each with a degeneracy of $g_i$. Let us imagine $n_j$ particles out of these $N$...
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### CFTs that are not modular invariant

Are there any 2d CFTs that do not have modular invariant partition functions? All the examples that I know of, like the free boson, WZW models, etc. have modular invariant partition functions.
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### Partition Function from Dispersion Relation in Molecular Dynamics

I’ve seen there are ways to compute the dispersion relation of a crystal from molecular dynamics. An example of how to do this is discussed in this question: Computing phonon dispersion from molecular ...
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### Complete the square for the generating functional of the Dirac field

Quote Peskin page 302 the Dirac generating function was $$Z[\bar \eta ,\eta ]=\int D\bar\psi D\psi\exp[i\int dx^4 (\bar\psi (i\gamma^\mu\partial_\mu -m )\psi+\bar\eta \psi+\bar\psi \eta)]$$ could be ...
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### How to write the spatial photon propagator of the generating function $Z[J]$ in QED?

There was a part in the lecture one didn't quite understand. (The charge $e=0$ in this post.) The partition function for massive fields such as scalar fields or the spin-1/2 fields were quite standard....
When doing thermal field theory, one can start with the definition of the (thermal) partition function $Z = Tr[e^{-\beta H}]$, and inserting a number of completness-relations, we can arrive at (I am ...