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The long-time asymptotic behavior is studied for a long-range variant of the Emch-Radin model of interacting spins. We derive upper and lower bounds on the expectation values of a class of observables. We prove analytically that the time scale at which the system relaxes to equilibrium diverges with the system size N, displaying quasistationary nonequilibrium behavior. This finding implies that, for large enough N, equilibration will not be observed in an experiment of finite duration.
We show that spatial resolved dissipation can act on Ising lattices molding the universality class of their critical points. We consider non-local spin losses with a Liouvillian gap closing at small momenta as $propto q^alpha$, with $alpha$ a positiv
We find the statistical weight of excitations at long times following a quench in the Kondo problem. The weights computed are directly related to the overlap between initial and final states that are, respectively, states close to the Kondo ground st
We present results of a Monte Carlo study for the ferromagnetic Ising model with long range interactions in two dimensions. This model has been simulated for a large range of interaction parameter $sigma$ and for large sizes. We observe that the resu
We consider a velocity field with linear viscous interactions defined on a one dimensional lattice. Brownian baths with different parameters can be coupled to the boundary sites and to the bulk sites, determining different kinds of non-equilibrium st
The aim of this short article is to convey the basic idea of the original paper [3], without going into too much detail, about how to derive sharp asymptotics of the gyration radius for random walk, self-avoiding walk and oriented percolation above the model-dependent upper critical dimension.