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… 

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