New proposal for numerical simulations of theta-vacuum-like systems.

We propose a new approach to perform numerical simulations of theta-vacuum-like systems, test it in two analytically solvable models, and apply it to CP3. The main new ingredient in our approach is the method used to compute the probability distribution function of the topological charge at theta=0. We do not get unphysical phase transitions (flattening behavior of the free energy density) and reproduce the exact analytical results for the order parameter in the whole theta range within a few percent.

Thermodynamics of self-gravitating systems with softened potentials

The microcanonical statistical mechanics of a set of self-gravitating particles is analyzed in a mean-field approach. In order to deal with an upper bounded entropy functional, a softened gravitational potential is used. The softening is achieved by truncating to N terms an expansion of the Newtonian potential in spherical Bessel functions. The order N is related to the softening at short distances. This regularization has the remarkable property that it allows for an exact solution of the mean-field equation. It is found that for N not too large the absolute maximum of the entropy coincides to high accuracy with the solution of the Lane-Emden equation, which determines the mean-field mass distribution for the Newtonian potential for energies larger than E(c) approximately -0.335GM(2)/R. Below this energy a collapsing phase transition, with negative specific heat, takes place. The dependence of this result on the regularizing parameter N is discussed.

Effect of angular momentum conservation in the phase transitions of collapsing systems.

The effect of angular momentum conservation within microcanonical thermodynamics is considered. This is relevant in self-gravitating systems, where angular momentum is conserved and the collapsing nature of the forces makes the microcanonical ensemble the proper statistical description of the physical processes. The microcanonical distribution function with nonvanishing angular momentum is obtained as a function of the coordinates of the particles. As an example, a simple model, introduced by Thirring long ago [Z. Phys. 235, 339 (1970)], is worked out. The phase diagram contains three phases: For low values of the angular momentum L the system behaves as the original model, showing a complete collapse at low energies and a convex intruder in the entropy. For intermediate values of L the collapse at low energies is not complete, and the entropy still has a convex intruder. For large L there is neither collapse nor anomalies in the thermodynamical quantities. A short discussion of the extension of these results to more realistic situations is given.