2005/05/27 by de Vega, H. J., Sanchez, N.
#Astrophysics (astro-ph) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.astro-ph/0505561
We provide a complete picture to the self-gravitating non-relativistic gas at thermal equilibrium using Monte Carlo simulations, analytic mean field methods (MF) and low density expansions. The system is shown to possess an infinite volume limit in the grand canonical (GCE), canonical (CE) and microcanonical (MCE) ensembles when (N, V) -> infty, keeping N/V1/3 fixed. We compute the equation of state (we do not assume it as is customary in hydrodynamics), as well as the energy, free energy, entropy, chemical potential, specific heats, compressibilities and speed of sound; we analyze their properties, signs and singularities. All physical quantities turn out to depend on a single variable eta = G m2 N /[V1/3 T that is kept fixed in the N -> infty and V -> infty limit. The system is in a gaseous phase for eta < etaT and collapses into a dense object for eta > etaT in the CE with the pressure becoming large and negative. At eta ≃ etaT the isothermal compressibility diverges and the gas collapses. Our Monte Carlo simulations yield etaT ≃ 1.515. We find that PV/[NT] = f(eta). The function f(eta) has a second Riemann sheet which is only physically realized in the MCE. In the MCE, the collapse phase transition takes place in this second sheet near etaMC = 1.26 and the pressure and temperature are larger in the collapsed phase than in the gaseous phase. Both collapse phase transitions (in the CE and in the MCE) are of zeroth order since the Gibbs free energy has a jump at the transitions.