Questions tagged [graph-theory]

DO NOT USE THIS TAG FOR graphs of a function.

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To calculate the resultant resistance of a circuit can you use all possible paths and assume they're parallel? [duplicate]

To calculate the resultant resistance of a circuit can you use all possible paths and assume they're parallel? Say I have a circuit like this: And I want to determine the resistance between x and y. ...
23 views

Measure of connectivity in Graph States

Given $G = (V,E)$, with the set of vertices $V$ and the set of edges $E$, the corresponding graph state is defined as $$|G\rangle = \prod_{(a,b)\in E} U^{\{a,b\}} |+\rangle ^{\otimes V}$$ where the ...
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Interpreting generating functional as sum of all diagrams

The generating functional is defined as: $$Z[J] = \int \mathcal{D}[\phi] \exp\Big[\frac{i}{\hbar}\int d^4x [\mathcal{L} + J(x)\phi(x)]\Big].$$ I know this object is used as a tool to generate ...
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Feynman diagrams with no lines crossing

What does it mean when we say a feynman diagram has no lines crossing? What are some examples of diagrams with and without lines crossing?
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Where can I find the configurations corresponding to the current largest max-cut values on $G$-set graphs?

I am looking for the configurations that are behind the max-cut value in many articles about solving the Ising problem/max-cut problem on graphs, but I can't seem to find any articles with this data ...
369 views

From Feynman diagram to electrical circuit in arXiv:hep-th/0308184 by Rajesh Gopakumar

I am asking this question on behalf of user furious.neutrino. I asked this question at Electrical Engineering Stack Exchange, but it has not received a reply, so I am duplicating it here. I think the ...
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General validity of the Linked Cluster Theorem in QFT for arbitrary correlation functions

In QFT, either at zero or finite temperature, the Linked Cluster Theorem (LCT) ensures that all disconnected diagrams appearing in the numerator of the interacting Green's function exactly cancel with ...
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What is the definition of $n$-loop 1PI diagrams in QFT? [closed]

What is the precise definition of a $n$-loop one-particle irreducible ($1$PI) diagram? For example, consider the following diagrams. Is the first diagram a $0$-loop $1$PI diagram? Is the second ...
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1 vote
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Mathematics of the star-mesh transformation

I'm trying to understand the star-mesh transform from a mathematical perspective. This transformation removes a node and by definition, the topology of the network changes, but the resulting network ...
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How to prove useful property of logarithm of generating functional in QFT?

How to prove that $\ln(Z(J))$ generates only connected Feynman diagrams? I can't find the proof of this statement, and have only met its demonstrations for case of 2- and 4-point.
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Dimension of the space of solutions in an electric circuit

Consider an electric circuit with dc sources ( voltage and current) and resistors. Write down the equations. In the most general case, the solution of the system is not unique. The set of solutions ...
188 views

Understanding the intermediate field method for the $\phi^4$ interaction

In Rivasseau's and Wang's How to Resum Feynman Graphs, on page 11 they illustrate the intermediate field method for the $\phi^4$ interaction and represent Feynman graphs as ribbon graphs. I had to ...
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Lattice theory in mathematics and physics [closed]

I have undertaken a project examining lattice model and trying to construct algorithm that could work on all lattice (in physical sense, or crystal structure). I notice there is a branch in ...
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What is the difference between scale-free network and small-world network? [closed]

What is the difference between scale-free network and small-world network? I can't understand from the definitions around the web if they are both the same name for one thing. Do both follow a power-...
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1 vote
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Research on ground state configuration of Ising model

I want to do mathematical research (algorithm construction and mathematical analysis) on Ising model ground state configuration. From what I know, the state of art research is using graph theory ...
464 views

Quantum graph theory: complex spectra

In quantum graph theory, what are the properties of a given graph to own complex conjugated complex eigenvalues, either finite or infinite? Spectral graph theory is as far as I know a not completely ...
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Spin Glass Transitions in Random Bond Ising Model (RBIM)

In brief, is there a list of spin glass transition properties for the RBIM on different lattices? Is there any know results about the relationships between these probabilities for a graph and its dual?...
160 views

Book reviewing current state of research on complex networks [closed]

Can anybody recommend a book reviewing the current state of knowledge and active research on complex networks? Not primarily a textbook but a true review of the field - ideally with references to ...
243 views

Graph Invariants and Statistical Mechanics

Many intuitive knot invariants including Jones' polynomial are inspired by statistical mechanics. Further profound connections have been explored between knot theory and statistical mechanics. I was ...
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What are the different methods for a resistor circuit that isn't parallel or series? [closed]

What are the different approaches to determine the equivalent resistance of nontrivial resistor networks in general, that cannot be reduced by the usual series and parallel rules? (The diagram below ...
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what is meant by "crossover phenomena"?

In many articles I read the term "crossover phenomena" and a lot of methodology discussed according to it, with little or no description about what is meant by it. Sometimes there is a connection to ...
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943 views

Properties of graph of subatomic particle interactions

Say there was some situation where you have a lot of subatomic particles interacting with each other and decided to draw (say, by joining Feynmann diagrams) those interactions- so that you got some ...
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Why are physicists interested in graph theory?

Can you tell me how graph theory comes into physics, and the concept of small world graphs? (inspired to ask from comment from sean tilson in): Which areas in physics overlap with those of social ...
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Which areas in physics overlap with those of social network theory for the analysis of the graphs?

I am studying social networks in terms of graph theory and linear algebra. I know that physicists have published and worked a lot in this field. This causes me to assume that there are sub-fields in ...
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