Mean-Field Behavior for Long- and Finite Range Ising Model, Percolation and Self-Avoiding Walk


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Please use this identifier to cite or link to this item:http://hdl.handle.net/2115/44912

Title:	Mean-Field Behavior for Long- and Finite Range Ising Model, Percolation and Self-Avoiding Walk
Authors:	Heydenreich, Markus Browse this author
	Hofstad, Remco van der Browse this author
	Sakai, Akira Browse this author →KAKEN DB
Keywords:	Lace expansion
	Ising model
	Percolation
	Self-avoiding walk
	Critical exponent
	Mean-field behavior
Issue Date:	2008
Publisher:	Springer
Journal Title:	Journal of Statistical Physics
Volume:	132
Issue:	6
Start Page:	1001
End Page:	1049
Publisher DOI:	10.1007/s10955-008-9580-5
Abstract:	We consider self-avoiding walk, percolation and the Ising model with long and finite range. By means of the lace expansion we prove mean-field behavior for these models if d >2(α ∧ 2) for self-avoiding walk and the Ising model, and d >3(α ∧ 2) for percolation, where d denotes the dimension and α the power-law decay exponent of the coupling function. We provide a simplified analysis of the lace expansion based on the trigonometric approach in Borgs et al. (Ann. Probab. 33(5):1886–1944, 2005).
Rights:	'The original publication is available at www.springerlink.com'
Type:	article
URI:	http://hdl.handle.net/2115/44912
Appears in Collections:	創成研究機構 (Creative Research Institution) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 坂井哲

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