# Statistical physics of loopy interactions: Independent-loop approximation and beyond

@article{Ramezanpour2015StatisticalPO, title={Statistical physics of loopy interactions: Independent-loop approximation and beyond}, author={Abolfazl Ramezanpour and Saman Moghimi-Araghi}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2015}, volume={92 3}, pages={ 032112 } }

We consider an interacting system of spin variables on a loopy interaction graph, identified by a tree graph and a set of loopy interactions. We start from a high-temperature expansion for loopy interactions represented by a sum of non-negative contributions from all the possible frustration-free loop configurations. We then compute the loop corrections using different approximations for the nonlocal loop interactions induced by the spin correlations in the tree graph. For distant loopy…

## One Citation

Forest expansion of two-body partition functions for sparse interaction graphs

- Mathematics, Computer Science
- 2020

It is shown that for sparse graphs, the partition function above a certain temperature Tc can be approximated by a graph polynomial expansion over forests of the interaction graph, and in the high-temperature regime, T can be obtained via a maximal spanning tree algorithm on a (given) weighted graph.

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