multicanonical

Multicanonical methods are Monte Carlo algorithms designed to overcome sampling barriers in systems with rugged energy landscapes. The central idea is to sample configurations with a weight that yields a nearly flat probability distribution of energy, thereby enabling transitions that are rare in canonical simulations.

Concretely, one adjusts a weight function W(E) to mimic the inverse density of states, such that the probability to visit energy E is proportional to 1/g(E). Since g(E) is unknown, W(E) is built iteratively, for example by modifying W(E) to flatten the energy histogram or by estimating the entropy S(E) = k_B ln g(E). Once W(E) converges, a production run collects data that can be reweighted to compute canonical averages at any temperature within the sampled range.

MUCA originated in lattice statistical mechanics through the work of Berg and Neuhaus in the early 1990s and is part of the family of generalized-ensemble methods, alongside simulated tempering and Wang-Landau sampling. It shares the goal of enhancing barrier crossing and enabling broad temperature scans.

Applications include spin models, polymers, and biomolecules, where MUCA helps to study phase transitions, folding pathways, and thermodynamics. The main advantage is that a single multicanonical simulation yields information across a wide temperature interval, avoiding multiple separate runs.

Challenges include determining accurate weight factors, ensuring convergence, and controlling statistical errors in reweighting, especially at the extremes of the energy (or temperature) range. Practical use requires discretization of energy and efficient update schemes.

Related concepts include the density of states g(E) and entropy S(E); MUCA data can be used to construct g(E) and to perform reweighting to obtain thermodynamic quantities as functions of temperature.