Spin systems from loop soups
van de Brug, T
Electronic Journal of Probability
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van de Brug, T., Camia, F., & Lis, M. (2018). Spin systems from loop soups. Electronic Journal of Probability, 23 (81)https://doi.org/10.1214/18-EJP200
We study spin systems defined by the winding of a random walk loop soup. For a particular choice of loop soup intensity, we show that the corresponding spin system is reflection-positive and is dual, in the Kramers-Wannier sense, to the spin system sgn(ϕ) where ϕ is a discrete Gaussian free field. In general, we show that the spin correlation functions have conformally covariant scaling limits corresponding to the one-parameter family of functions studied by Camia, Gandolfi and Kleban (Nuclear Physics B 902, 2016) and defined in terms of the winding of the Brownian loop soup. These functions have properties consistent with the behavior of correlation functions of conformal primaries in a conformal field theory. Here, we prove that they do correspond to correlation functions of continuum fields (random generalized functions) for values of the intensity of the Brownian loop soup that are not too large.
The research of ML was funded by EPSRC grants EP/I03372X/1 and EP/L018896/1.
External DOI: https://doi.org/10.1214/18-EJP200
This record's URL: https://www.repository.cam.ac.uk/handle/1810/292531