Marked Gibbs measures via cluster expansion

作者: Tobias Kuna , Yuri Kondratiev , Jose Luis Silva

DOI:

关键词: Riesz–Markov–Kakutani representation theoremMathematical analysisMathematicsState space (physics)Locally compact spaceRadon measurePure mathematicsConvex metric spaceSeparable spaceInjective metric spaceSpace (mathematics)

摘要: We give a sufficiently detailed account on the construction of marked Gibbs measures in high temperature and low fugacity regime. This is proved for wide class underlying spaces potentials such that stability integrability conditions are satisfied. That is, state space we take locally compact separable metric $X$ $S$ mark space. framework allowed us to cover several models classical quantum statistical physics. Furthermore, also show how extend more general as e.g., standard Borel spaces. The based method cluster expansion.

参考文章(21)
Hans Föllmer, Phase transition and Martin boundary Séminaire de probabilités de Strasbourg. ,vol. 9, pp. 305- 317 ,(1975) , 10.1007/BFB0103000
Hans-Otto Georgii, Gibbs Measures and Phase Transitions ,(1988)
Hiroaki Shimomura, Poisson measures on the configuration space and unitary representations of the group of diffeomorphisms Journal of Mathematics of Kyoto University. ,vol. 34, pp. 599- 614 ,(1994) , 10.1215/KJM/1250518934
Oystein Ore, Theory of graphs ,(1962)
Silvano Romano, Valentin A. Zagrebnov, Orientational ordering transition in a continuous-spin ferrofluid Physica A-statistical Mechanics and Its Applications. ,vol. 253, pp. 483- 497 ,(1998) , 10.1016/S0378-4371(97)00669-9
Computer Simulation Studies of Anisotropic Systems IV. The Effect of Translational Freedom Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 373, pp. 111- 130 ,(1980) , 10.1098/RSPA.1980.0139
DAVID RUELLE, Cluster Property of the Correlation Functions of Classical Gases Reviews of Modern Physics. ,vol. 36, pp. 580- 583 ,(1964) , 10.1103/REVMODPHYS.36.580
Chris Preston, Canonical and microcanonical Gibbs states Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete. ,vol. 46, pp. 125- 158 ,(1979) , 10.1007/BF00533255
Yuri Kondratiev, Ludwig Streit, Jose Luis Silva, Differential Geometry on Compound Poisson Space arXiv: Functional Analysis. ,(1999)
S Albeverio, Yu.G Kondratiev, M Röckner, Analysis and Geometry on Configuration Spaces: The Gibbsian Case Journal of Functional Analysis. ,vol. 157, pp. 242- 291 ,(1998) , 10.1006/JFAN.1997.3215