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== Motivation ==
The problem of the critical slowing-down affecting local processes is of fundamental importance in the study of second-order [[Phase transition|phase transitions]] (like ferromagnetic transition in the Ising model) as increasing the size of the system in order to reduce finite-size effects has the disadvantage of requiring a far larger number of moves to reach thermal equilibrium.
Indeed the correlation time <math>\tau</math> usually increases as <math>L^z</math> with <math>z\simeq 2</math> or greater; since, to be accurate, the simulation time must be <math>t\gg\tau</math>, this is a major limitation in the size of the systems that can be studied through local algorithms. SW algorithm was the first to produce unusually small values for the dynamical critical exponents: <math>z=0.35</math> for the 2D Ising model (<math>z=2.125</math> for standard simulations); <math>z=0.75</math> for the 3D Ising model, as opposed to <math>z=2.0</math> for standard simulations.
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