EXACT DENSITY-OF-STATES AND ITS CRITICAL-BEHAVIOR

We propose a fast algorithm for the exact computation of the density o f states for arbitrary discrete systems on intermediate-size lattices. Results for the Ising model on lattices up to 13 x 13 are presented. We also discuss how signals for phase transitions may be observed by i nspecting the density of states directly, and verify this with the num erical data for the Ising model. This procedure is based on the classi cal view of the density of states as the exponential of the entropy. P hase transition are then characterized by ''straight sections'' in the entropy, considered as a function of the energy. It is found that sec ond- as well as first-order phase transitions may be so described, the difference between the two being in the way the length of the straigh t section goes to infinity with the size of the system. This viewpoint leads then to a short and physically transparent derivation of the Jo sephson inequality for critical exponents.