Graded Cluster Expansion for Lattice Systems
نویسندگان
چکیده
منابع مشابه
Graded cluster algebras
In the cluster algebra literature, the notion of a graded cluster algebra has been implicit since the origin of the subject. In this work, we wish to bring this aspect of cluster algebra theory to the foreground and promote its study. We transfer a definition of Gekhtman, Shapiro and Vainshtein to the algebraic setting, yielding the notion of a multi-graded cluster algebra. We then study gradin...
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Abstract Cluster Expansion with Application to Statistical Mechanical Systems
CLUSTER EXPANSION WITH APPLICATIONS 3 Assumption 2. There exists a nonnegative function a on X such that for almost all x ∈ X, ∫ d|μ|(y) |ζ(x, y)| e 6 a(x). In order to guess the correct form of a, one should consider the left side of the equation above with a(y) ≡ 0. The integral may depend on x; a typical situation is that x is characterized by a length l(x), which is a positive number, so th...
متن کاملAbstract Cluster Expansion with Applications to Statistical Mechanical Systems
CLUSTER EXPANSION WITH APPLICATIONS 3 In order to guess the correct form of a, one should consider the left side of the equation above with a(y) ≡ 0. The integral may depend on x; a typical situation is that x is characterized by a length l(x), which is a positive number, so that the left side is roughly proportional to l(x). This suggests to try a(x) = cl(x), and one can then optimize on the v...
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Experts do not always feel very comfortable when they ha vt! to give precise nunterica I estimations of cena inty degrees. In this paper we present a qualitative approach which allows for atraching parti ally ordered symbolic grades to logical formulas. Uncertain inform ati on is expressed by means of parameterized mod a I operators. We propo se a sema ntics for this multimodal logic and give a...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2005
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-005-1360-3