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### Physical meaning of partition function in QFT

When we have the generating functional $Z$ for a scalar field Z(J,J^{\dagger}) = \int{D\phi^{\dagger}D\phi \; \exp\Big[{\int L+\phi^{\dagger}J(x)+J^{\dagger}(x)}\phi\Big]}, \end{...
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### Why does this formula for the partition function not include the multiplicity?

I am having problems understanding the formulas used for describing the partition functions and the probability distributions for canonical ensembles. In the first case I have two formulas for the ...
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### How to write any partition function?

So I am familiar with the derivation of the partition function for a canonical and a grand canonical ensemble. I have seen definitions of the partition function for some of the quantum counterparts of ...
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### What are alternative ways to think about transfer matrix as used in Ising model?

I recently learned about how to find the partition function of Ising model using Transfer Matrix method. At my level of understanding things, it is a trick that happens to work! I would like to ...
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### Does the canonical partition function count microstates?

The microcanonical partition function is the density of states. The canonical one, from a dimensional point of view, is still a number of states, but does it actually count microstates? I tried ...
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### Mono-atomic gas particles coupled by spring forces don't care how many particles are involved?

I calculated the partition function of $N$ classical atoms of identical mass $m$ who all experience a mutual spring forces with identical spring constant $k$. The Hamilton is \begin{align} H = \dfrac{...
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Is the partition function of a 3D vibrating string a sum of discrete energies, an integral of an energy continuum, or both? $$Z_{\text{disc}} = \sum_{k=1}^{\infty}g_ke^{-\beta E_k}$$ or $$Z_{\text{... 1answer 83 views ### A trace formula of two noncommutative operators In many cases of quantum many-body problems, the Hamiltonian H can always be divided into two parts, i.e. H_0 and H'. In this occasion, one can systemically calculate the partition function ... 1answer 81 views ### Partition function is simply temperature if possible sub system energy is continuous? Partition function is$$Z=\sum_j\exp\left(-\frac{\epsilon_j}{kT}\right)$$a sum over all possible energy levels \epsilon_1,\epsilon_2, ..., \epsilon_M. There must be a finite number of choices ... 1answer 381 views ### About the factorial N! in the partition function After reading these posts: Why is the partition function divided by (h^{3N} N!)? , What is the resolution to Gibb's paradox?, and some of these: http://arxiv.org/abs/1012.4111 , http://bayes.... 1answer 84 views ### Einstein model for thermal capacity of solids and indistinguishability of the oscillators Albert Einstein's theory of thermal capacity of a solids makes the assumption that a crystal is made up from oscillators which of course oscillate, in all three directions. Thus, for N atoms of the ... 1answer 275 views ### Difference in partition function of classical and quantum Ideal gas First, I have read this question:What is meant by the term "single particle state" There is an analysis going on in my book (Mandle F. Statistical Physics) that has brought me in a ... 4answers 560 views ### Why is the partition function divided by (h^{3N} N!)? When computing partition functions for classical systems with N particles with a given Hamiltonian H I've seen some places writing it as$$Z = \dfrac{1}{h^{3N} N!}\int e^{-\beta H(p,q)}dpdq$$... 1answer 187 views ### What is the definition of 'relative population' in context of partition function? In statistical mechanics, what is the definition (or mathematical definition) when authors refer to relative population in the case of a classical particle system? 1answer 62 views ### is it necessarily true that the partition function Z (with degeneracies)  =1? The partition function with degnerate energies is$$\text{Z}=\sum _ig_ie^{{-E_i}/{k_BT}}.$$Because the partition function Z is defined as the normalisation constant, does Z always = 1? 2answers 158 views ### Conceptual explanation of the Single particle partition function The Single particle partition function is defined mathematically as$$\text{Z=$\sum$}g_ie^{\left(\frac{-E_i}{K_BT}\right)}$$But what is the physical interpretation of the partition function and it'... 1answer 65 views ### Superstring vacuum amplitude on the torus My question is how to obtain the superstring (Type II A and B) vacuum amplitudes on a torus. They are given in Polchinski's String Theory Vol. 2 equation (10.7.9):$$Z_\psi^{\pm}=\frac{1}{2}[Z^0_0(\...
Ordinary generating function can be used to solve combinatorial enumeration problems. Now if the energy levels are discrete, say $g_i$, and if one want to count how many ways one can add up $g_i$ ...