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Continuum limit in lattice models
An animated example of a Brownian motion -like random walk on a torus . In the scaling limit, random walk approaches the Wiener process according to Donsker's theorem .
In mathematical physics and mathematics , the continuum limit or scaling limit of a lattice model characterizes its behaviour in the limit as the lattice spacing goes to zero. 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 .
Terminology [ edit ]
The term continuum limit mostly finds use in the physical sciences, often in reference to models of aspects of quantum physics , while the term scaling limit is more common in mathematical use.
Application in quantum field theory [ edit ]
A lattice model that approximates a continuum quantum field theory in the limit as the lattice spacing goes to zero may correspond to finding a second order phase transition of the model. This is the scaling limit of the model.
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 φ4 , World Scientific (Singapore, 2001) ; Paperback ISBN 981-02-4658-7 (also available online )
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● T h i s p a g e w a s l a s t e d i t e d o n 1 3 J a n u a r y 2 0 2 4 , a t 0 0 : 2 0 ( U T C ) . ● T e x t i s a v a i l a b l e u n d e r t h e C r e a t i v e C o m m o n s A t t r i b u t i o n - S h a r e A l i k e L i c e n s e 4 . 0 ;
a d d i t i o n a l t e r m s m a y a p p l y . B y u s i n g t h i s s i t e , y o u a g r e e t o t h e T e r m s o f U s e a n d P r i v a c y P o l i c y . W i k i p e d i a ® i s a r e g i s t e r e d t r a d e m a r k o f t h e W i k i m e d i a F o u n d a t i o n , I n c . , a n o n - p r o f i t o r g a n i z a t i o n . ● P r i v a c y p o l i c y ● A b o u t W i k i p e d i a ● D i s c l a i m e r s ● C o n t a c t W i k i p e d i a ● C o d e o f C o n d u c t ● D e v e l o p e r s ● S t a t i s t i c s ● C o o k i e s t a t e m e n t ● M o b i l e v i e w
