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We describe an efficient Monte Carlo algorithm using a random walk in energyspace to obtain a very accurate estimate of the density of states for classicalstatistical models. The density of states is modified at each step when theenergy level is visited to produce a flat histogram. By carefully controllingthe modification factor, we allow the density of states to converge to the truevalue very quickly, even for large systems. This algorithm is especially usefulfor complex systems with a rough landscape since all possible energy levels arevisited with the same probability. In this paper, we apply our algorithm toboth 1st and 2nd order phase transitions to demonstrate its efficiency andaccuracy. We obtained direct simulational estimates for the density of statesfor two-dimensional ten-state Potts models on lattices up to $200 \times 200 $and Ising models on lattices up to $256 \times 256$. Applying this approach toa 3D $\pm J$ spin glass model we estimate the internal energy and entropy atzero temperature; and, using a two-dimensional random walk in energy andorder-parameter space, we obtain the (rough) canonical distribution and energylandscape in order-parameter space. Preliminary data suggest that the glasstransition temperature is about 1.2 and that better estimates can be obtainedwith more extensive application of the method.Comment: 22 pages (figures included

Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram