Spanning forests and OSP(N vertical bar 2M)-invariant sigma-models

作者：Caracciolo Sergio^*; Sokal Alan D; Sportiello Andrea

来源：Journal of Physics A-Mathematical and Theoretical, 2017, 50(11): 114001.

DOI：10.1088/1751-8121/aa59bc

• spanning forests
• supersymmetric sigma-models
• Potts model

The present paper is part of our ongoing work on OSP(N vertical bar 2M) supersymmetric sigma-models, their relation with the Potts model at q = 0 and spanning forests, and the rigorous analytic continuation of the partition function as an entire function of N - 2M, a feature first predicted by Parisi and Sourlas in the 1970s. Here we accomplish two main steps. First, we analyze in detail the role of the Ising variables that arise when the constraint in the OSP(1 vertical bar 2) model is solved, and we point out two situations in which the Ising and forest variables decouple. Second, we establish the analytic continuation for the OSP(N vertical bar 2M) model in some special cases: when the underlying graph is a forest, and for the Nienhuis action on a cubic graph. We also make progress in understanding the series-parallel graphs.

• 出版日期2017-3-17