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multicanonical ensemble
In statistics and physics, multicanonical ensemble (also called multicanonical sampling or flat histogram) is a Markov chain Monte Carlo sampling technique that uses the Metropolis–Hastings algorithm to compute integrals where the integrand has a rough landscape with multiple local minima. It samples states according to the inverse of the density of states,〔 which has to be known a priori or be computed using other techniques like the Wang and Landau algorithm.〔 Multicanonical sampling is an important technique for spin systems like the Ising model or spin glasses.〔〔〔
==Motivation==
In systems with a large number of degrees of freedom, like spin systems, Monte Carlo integration is required. In this integration, importance sampling and in particular the Metropolis algorithm, is a very important technique.〔 However, the Metropolis algorithm samples states according to where beta is the inverse of the temperature. This means that an energy barrier of on the energy spectrum is exponentially difficult to overcome.〔 Systems with multiple local energy minima like the Potts model become hard to sample as the algorithm gets stuck in the system's local minima.〔 This motivates other approaches, namely, other sampling distributions.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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