New Numerical Algorithms for Critical Phenomena (Multi-Grid Methods and All That)

Monte Carlo computations in statistical mechanics and quantum field theory have been greatly hampered by critical slowing-down. We review recent progress in devising new Monte Carlo algorithms having radically reduced critical slowing-down. We discuss “collective-mode” algorithms (multi-grid and Swendsen-Wang) for spin systems and lattice field theories, and algorithms for the self-avoiding walk. We also discuss an algebraic multi-grid algorithm for solving Kirchhoff’s equations in the random-resistor problem.

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