# Questions tagged [partition-function]

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### $N$ particles in a box [closed]

I am writing to ask about the problem: $N$ particles in a box.(particles are treated as ideal gas) As you know, $N$ particles will enter the N boxes one by one. First, I entitle the $N$ boxes are ...
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### Partition function for two systems

The goal. Calculate the partition function of the following systems: A gas of $N$ non-interacting distinguishable particles with non-degenerate energy levels $E_0=0$ and $E_1=\epsilon$; A chain of $N$...
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### How can I show that $1/N$ expansion for large $N$ matrix models have a string theoretical perturbation expansion?

While surfing through some further reading suggestions on string theory, I stumbled upon this slide from a talk by Nathan Seiberg. I wanted to derive the main argument by applying a perturbation ...
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### One-loop effective action for scalar field on the curved background in large potential

I hope to compute a functional integral $Z=\int \mathcal{D}\phi\,\, e^{-S[\phi]}$ with an action $$S[\phi]=\int d^2x \sqrt{g}\Big((\nabla \phi)^2+\frac{1}{\lambda}M^2(x) \phi^2\Big)$$ The scalar field ...
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### Partition function in quantum field theory

Why does the partition function include current term in free scalar field $$Z[J] = \int \mathcal{D}\phi \, e^{i \left(S[\phi] + \int d^4x \,J(x) \phi(x) \right)}~$$
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### Partition function for 4 spins

I was reading some notes by John Chalker on order by disorder and encountered a classical spins partition function calculation. I could not follow the integration, i.e. obtaining eqn. (1.7) from (1.5) ...
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### A closer look on the derivation of the susceptibility in the Ising-Model

The susceptibility $\chi$ can be defined as $$\chi = \frac{\partial \langle M \rangle}{\partial H}, \tag{1}$$ where $\langle M \rangle$ is defined as the average magnetization and thus can be written ...
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### What is the entropy and/or equation of state of a partition function such as $Z=\int D\phi \exp (i S[\phi]/\hbar)$?

At this link https://en.wikipedia.org/wiki/Partition_function_(mathematics), it is claimed that the following partition function: $$Z=\int D\phi \exp (-\beta H[\phi]) \tag{1}$$ is a consequence of ...
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### How does anomaly inflow work in terms of the eta invariant?

I'm trying to understand the non-perturbative picture of anomaly inflow, mainly following these two articles by Witten and Yonekura:  - https://arxiv.org/pdf/1909.08775.pdf ,  - https://arxiv....
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### About the various ensembles in Thermodynamics

The properties of a system in thermodynamical equilibrium are described by a partition function: $$\mathcal{Z} = \text{Tr} \ e^{-\beta E} = \sum_n e^{-\beta E_n}$$ This defines so called canonical ...
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### Where does the radius integral go in the partitition function?

I am confused about a given solution for the following exercise: A thermodynamic system consists of N atoms in the Volume V. Every atom has a magnetic moment. The hamiltonian can be written as a sum ...
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### Canonical ensemble: Why do I lose dependency on the number of particles N here?

I have a problem understanding the solution of an exercise that deals with a gas in the framework of the canonical ensemble. Because I'm not a native english speaker some sentences might sound a bit ...
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### How are the saddle-point equations derived in the single random matrix model?

In this question, I'm referring to a specific step in https://arxiv.org/abs/hep-th/9306153. I want to reproduce equation (2.4) on page 15. I think I lack the experience required for dealing with ...
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### Chemical potential in canonical partition function

I'm a bit confused on the interpretation of the chemical potential in a canonical ensemble (a system which can only exchange energy with a reservoir but not particles). Here is what I think I know: ...
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### How to deal with integral operators in the action, in the path integral of a field theory?

One could imagine adding to the free action of a scalar field theory some non-local operators given as integrals over the base manifold (or over the boundary) of some smooth function of the scalar ...
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### Equation of state of a path integral

How does one take the equation of state of a path integral? In "discrete" statistical physics, one has this partition function: $$Z=\sum_{i}\exp(-\beta E[i])$$ And the equation of state is the ...