# 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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### Changing variable in path integral

Good evening, I am learning about path integrals in QFT and I was wondering, can you simplify the path integral by shifting the fields? To make it more clear I will give you an example. Suppose that I ...
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### Does a CFT need a UV regulator?

I have a very basic question about conformal field theory: Does the partition function need a UV regulator, or is it finite even without? That is, does $\int D\phi \exp(-S)$ converge, or do we need to ...
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### Partition Function and Expected value of dipole moment

I have a cubic lattice, and I am trying to find the partition function and the expected value of the dipole moment. I represent the dipole moment as a unit vector pointing to one the 8 corners of the ...
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### Doubt in the expression of partition function of a general canonical ensemble

Suppose we have a system $S$ connected to a bath $B$. The combined system forms a microcanonical ensemble. Suppose the energy of the combined system is $E_T$. So, $E_S+E_B=E_T$. The probability of ...
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### What are $\mathcal{F}_g$ in string theory?

I was reading an article and came up on $\mathcal{F}_g$. Namely, it was in the following equation, $$\psi_{top} = \exp(\sum_g \mathcal{F}_g)$$ where I believe the $g$ denotes the genus of the topology ...
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### Boltzmann distribution and probability of finding the system with specific energy

For sake of simplicity assume classical discrete systems. If we have a system ($\text{S}$) coupled to a reservoir ($\text{R}$), then a microstate of the combined (isolated with fixed energy $E$) ...
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### Generalized partition function with angular momentum

I'm studying statistical mechanics, and I found this problem in my study material: Suppose you have a gas consisting of N identical non-interacting atoms in a harmonic trap. Consider its Hamiltonian ...
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### The Partition Function of $0$-Dimensional $\phi^{4}$ Theory

My question is related with this question. Several years ago, I posted an answer to the question, and the author of the reference removed the link permanently, now I have no clue what's going on. In ...
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### Is it OK to do this manipulation at the partition function level? (auxiliary fields in quadratic gravity)

Background I am working with the following action in the Euclidean signature ($C^2$ is the Weyl quadratic term): \begin{equation} S_B = -\frac{1}{2\kappa^2}\int d^4x\sqrt{g}\left(2\Lambda_C+\zeta R-\...
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### String partition function

Hey I am a bit confused because when reading physics papers I encounter the free energy as a generating function of topological invariants as integrals over certain compactified moduli spaces. For ...
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### Ideal Fermi gas close to $T=0 \rm K$

I am reading about the behaviour of ideal Fermi gas close to $T=0K$ from Kardar's Statistical Mechanics. In the paragraph which I have highlighted, we have the inyegral representation of $f_m^{-}(z)$....
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I am reading ideal quantum gas from Kardar's Statistical Mechanics. $VII.35$ is the representation of pressure, number density and energy density in the form of $f_m^{\eta}$. $z=e^{\beta\mu}$ where \$\...