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9 votes
1 answer
1k views

Correlation-Function for Random Graph Ising Model

For non-Ising'ers: Given a graph, we study the probability-distribution on the set of colorings ("Spin-up" and "-down") generated by a given correlation ("force to equality") between adjacient nodes (...
Simon Lentner's user avatar
5 votes
1 answer
222 views

Switching oriented paths in a graph

Consider an oriented graph (e.g. a finite part of the standard grid with some random orientations). Each minute the following operation takes place: we choose uniformly randomly an ordered pair $(A,B)...
Nikita Kalinin's user avatar
3 votes
1 answer
108 views

Expected size of matchings in a cubic graph

Let $G$ be a random cubic graph on $n$ vertices. Let $M$ be the set of (not necessarily maximum) matchings of $G$. What is the expected size (i.e. number of edges) of an element of $M$? In other ...
LeechLattice's user avatar
  • 9,501
3 votes
0 answers
229 views

For Ising models on finite graphs, is the gradient of Z (w/r/t coupling and field) easier to compute than Z?

Suppose we have a graph $G$ with $n$ vertices, edgeset $E$, $\mathcal{X}=\{1,-1\}^n$. The partition function of the spin-1/2 Ising model on $G$ is $$Z(J,h)=\sum_{x\in \mathcal{X}} \exp\left(J \sum_{(...
Yaroslav Bulatov's user avatar