We diagonalize the XX model with a finite number of spins and periodic boundary conditions. We solve for the ground state, focus on the rapidity of the convergence to the thermodynamic limit and study the features of multipartite entanglement.

Bose-Einstein condensation (BEC) of a noninteracting Bose gas of N particles in a two-dimensional box with Dirichlet boundary conditions is studied. Confirming previous work, we find that BEC occurs at finite N at low temperatures T without the occurrence of a phase transition. The conventionally-defined transition temperature T(E) for an infinite three-dimensional (3D) system is shown to corre...

We discuss the underlying connections among the thermodynamic properties of short-ranged spin glasses, their behavior in large finite volumes, and the interfaces that separate different pure states, and also ground states and low-lying excitations.

The atmosphere and ocean primitive equation, which are consist of fluid equations, thermodynamic equations state play a important role for numerical weather precdiction.In an earlier work we have shown the finite-time blowup 3-D oceanic atmospheric dynamics without viscosity by using method self-similar solutions.In this paper show that certain class initial data, corresponding smooth solutions...