### On spin systems, loop representations, and random partitions

Probability Seminar

2nd June 2023, 3:30 pm – 4:30 pm

Fry Building, 2.04

Some classical and quantum spin systems (such as the Heisenberg models) are equivalent

to probabilistic models of random loops. Looking at the lengths of the loops, we get measures

on random partitions. It is conjectured that for quantum systems in dimensions 3 or greater,

the measure on random partitions is always a Poisson-Dirichlet distribution.

I will explain what is known and what is expected in this context. I will also address the

question of characterising random partition through “random colouring”. This is indirectly related

to symmetries of the spin systems.

Based on joint works with C. Benassi, J. Björnberg, C. Mailler, P. Mörters.

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