Efficient simulations of epidemic models with tensor networks: Application to the one-dimensional susceptible-infected-susceptible model.

The contact process is an emblematic model of a nonequilibrium system, containing a phase transition between inactive and active dynamical regimes. In the epidemiological context, the model is known as the susceptible-infected-susceptible model, and it is widely used to describe contagious spreading. In this work, we demonstrate how accurate and efficient representations of the full probability distribution over all configurations of the contact process on a one-dimensional chain can be obtained by means of matrix product states (MPSs).

The Stochastic Complexity of Spin Models: Are Pairwise Models Really Simple?

Models can be simple for different reasons: because they yield a simple and computationally efficient interpretation of a generic dataset (e.g., in terms of pairwise dependencies)-as in statistical learning-or because they capture the laws of a specific phenomenon-as e.

Fractality in nonequilibrium steady states of quasiperiodic systems.

We investigate the nonequilibrium response of quasiperiodic systems to boundary driving. In particular, we focus on the Aubry-André-Harper model at its metal-insulator transition and the diagonal Fibonacci model. We find that opening the system at the boundaries provides a viable experimental technique to probe its underlying fractality, which is reflected in the fractal spatial dependence of simple observables (such as magnetization) in the nonequilibrium steady state.