# Scaling limit

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In physics or mathematics, the **scaling limit** is a term applied to the behaviour of a lattice model in the limit of the lattice spacing going to zero. A lattice model which approximates a continuum quantum field theory in the limit as the lattice spacing goes to zero corresponds to finding a second order phase transition of the model. This is the scaling limit of the model. It is often useful to use lattice models to approximate real-world processes, such as Brownian motion. Indeed, according to Donsker's theorem, the discrete random walk would, in the scaling limit, approach the true Brownian motion.

## See also[edit]

## References[edit]

- H. E. Stanley,
*Introduction to Phase Transitions and Critical Phenomena* - H. Kleinert,
*Gauge Fields in Condensed Matter*, Vol. I, " SUPERFLOW AND VORTEX LINES", pp. 1–742, Vol. II, "STRESSES AND DEFECTS", pp. 743–1456, World Scientific (Singapore, 1989); Paperback ISBN 9971-5-0210-0*(also available online: Vol. I and Vol. II)* - H. Kleinert and V. Schulte-Frohlinde,
*Critical Properties of φ*, World Scientific (Singapore, 2001); Paperback ISBN 981-02-4658-7^{4}-Theories*(also available online)*

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