# 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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### Can we discuss about setting partition function of 1:1 salt electrolyte?

I have 1:1 salt whose density is described by $\rho(r) = \sum\limits_{i=+,-}\sum\limits_{j=1}^{N_{i}}q_{i}\delta(r-r_{ij})$, where $i$ denotes ion species such as +, - and $j$ represents number of $j$ ...
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### Problem with different expressions of functional determinant

This question is a follow-up of my previous one, after having done some calculations. In this previous question I used a minimal example of my problem with $\det(\Delta) = \det(\partial^2+A(x))$, but ...
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### Functional determinant: linking Series, Heat-Kernel and Zeta function

I would like to express a functional determinant as a series of diagrams, using the zeta function renormalization applied to the heat-kernel method, but I don't know if it's possible. Let me explain: ...
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### Operator insertions vs boundary conditions in AdS/CFT

This question is motivated by AdS/CFT, but really it's just about AdS quantum gravity. Consider quantum gravity in asymptotically AdS spacetime. For simplicity, assume there are no matter fields: the ...
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### 2 State canonical ensemble partition function where number of particles in each state is known

If we're asked to find the partition function for a two state system with energies $E_1$ and $E_2$ for $N$ indistinguishable, independent classical particles, then it makes sense to me that the ...
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### Path integral in Lattice gauge theory with fixed gauge really the same as without fixing the gauge?

In 1 the question why in lattice gauge theories with gauge group $G$, there was no need for gauge fixing to obtain finite path integrals was answered. Thus observables could be calculated as \begin{...
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### Physical interpretation of the asymptotics of partition function in string theory

I would like to understand the physical interpretation of the asymptotic expansion of a partition function. The QCD partition function with gauge group $SU(N)$ as $N$ is large has been shown by Gross ...
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### Why is the free energy unitless when taking the thermodynamic limit?

Why is the (Helmhotz) free energy unitless when taking the thermodynamic limit? Given the partition function $Z$ of a (finite size) system, the free energy is given by $F =-kT \log[Z]$, where $k$ is ...
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### Derivation of the Canonical Ensemble

One of the common derivations of the canonical ensemble goes as follows: Assume there is a system in the contact with heat reservoir which together form an isolated system. Heat can be exchanged ...
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### What is a symmetry of the generating functional, and what is the significance?

I cannot find a definition for a symmetry of the generating functional in Quantum Field Theory: $$Z[J] = \int \mathrm d \mu \, \exp\left\lbrace i S[J] \right\rbrace \, .$$ I know it's a simple ...
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### Partition function for weakly interacting gases

I'm studying the Susskind lecture on statistical mechanics. A potential energy of pairwise interactions has been defined: $$\sum_{n>m}U(|x_n -x_m|)$$ We want to calculate the partition function, ...
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### Partition Function of a Hydrogen Atom - How it is derived?

It is well-known that the Partition Function of Hydrogen Atom diverges if we calculate in naive manner. And I could find the partition function named Brillouin-Planck-Larkin partition function which ...
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### Correlation Function and Generating Functional in QED

Peskin and Schroeder (1995, p.82 and p.292) define the two-point correlation function of a $\phi^4$ theory as $$\langle \Omega|T\{\phi(x)\phi(y)\}|\Omega\rangle\tag{4.10}$$ and the generating ...
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In their paper, Callan and Wilczek claim to derive from the thermal entropy $$S_\text{thermal} = -\left(\beta\frac{\partial}{\partial\beta}-1\right)\ln(\mathcal{Z})$$ a geometric entropy which is ...
I have a doubled-stranded dna molecule. The molecule has N links, each of which can be one of two states: a closed state and an open state with energy $\epsilon$. A link can be open only if the link ...