Discrete approximations to vector spin models

We strengthen a result from Kulske and Opoku (2008 Elecavn. J. Probab. 13 1307-44) on the existence of effective interactions for discretized continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of discretizing contin...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2011-11, Vol.44 (47), p.475002-11
Main Authors: van Enter, Aernout C D, Külske, Christof, Opoku, Alex A
Format: Article
Language:English
Subjects:
Approximation
Exact sciences and technology
Mathematical analysis
Mathematical models
Physics
Two dimensional
Vectors (mathematics)
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Summary:We strengthen a result from Kulske and Opoku (2008 Elecavn. J. Probab. 13 1307-44) on the existence of effective interactions for discretized continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of discretizing continuous-spin models, and show that except for very low temperatures, they behave similarly in two dimensions. We also discuss some possibilities in higher dimensions.
ISSN:1751-8121
1751-8113
1751-8121
DOI:10.1088/1751-8113/44/47/475002