Quantum circuits offer a versatile platform for simulating digital quantum dynamics and
uncovering novel states of non-equilibrium quantum matter. One principal example are …

We introduce a family of loop soup models on the hypercubic lattice. The models involve
links on the edges, and random pairings of the link endpoints on the sites. We conjecture …

We present a systematic analysis of quantum Heisenberg-, xy-and interchange models on
the complete graph. These models exhibit phase transitions accompanied by spontaneous …

We present a detailed study of the equilibrium properties and stochastic dynamic evolution
of the U (1)-invariant relativistic complex field theory in three dimensions. This model has …

We study a spatial model of random permutations on trees with a time parameter T>0, a
special case of which is the random stirring process. The model on trees was first analysed …

These notes describe several loop soup models and their {\it universal behaviour} in
dimensions greater or equal to 3. These loop models represent certain classical or quantum …

We give estimates of the critical parameter for random loop models that are related to
quantum spin systems. A special case of the model that we consider is the interchange-or …

We estimate the critical temperature of a family of quantum spin systems on regular trees of
large degree. The systems include the spin-1 2 1 2 XXZ model and the spin-1 nematic …

We consider a class of random loop models (including the random interchange process) that
are parametrised by a time parameter $\beta\geq 0$. Intuitively, larger $\beta $ means more …

This thesis deals with higher dimensional phenomena in\textit {random walk loop soups}
which are statistical mechanics systems of closed interacting random walk trajectories on the …