Monte Carlo Studies of the Globally-Coupled Ising Model

Daniel Shai

Published Jan 1, 2007• 0 citations

Abstract

•Goal: determine the density of states (g[E]): the number of spin configurations producing an energy, E. • In an unbiased random walk in energy space, realized by randomly flipping spins, the histogram of the energy distribution (h[E]) converges to the density of states (g[E]), but too slowly to be practical. •When the random walk is biased inversely to g[E] so that h[E] becomes flat, g[E] is constructed to within an error ∝ ln[f ] if at each energy visited, g[E] is redefined as g[E]× f . If f is incrementally reduced to = 1, g[E] becomes exact. •Random walk acceptance bias: P [E1 → E2] = min g[E1] g[E2] , 1 

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