Quantum Heisenberg models and their probabilistic representations
Quantum Heisenberg models and their probabilistic representations
These notes give a mathematical introduction to two seemingly unrelated topics: (i) quantum spin systems and their cycle and loop representa- tions, due to T oth and Aizenman-Nachtergaele; (ii) coagulation-fragmentation stochastic processes. These topics are nonetheless related, as we argue that the lengths of cycles and loops eectively perform a …