Reflection Positivity of the Random-Cluster Measure Invalidated for Noninteger q
作者： Marek Biskup
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摘要: We consider the random-cluster Potts measure on a lattice torus that weights each connected component by positive number q. show, constructing counterexample, this is not reflection-positive unless q integer.
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sci-hub.se 参考文章(10)
C.M. Fortuin, P.W. Kasteleyn, On the random-cluster model: I. Introduction and relation to other models Physica D: Nonlinear Phenomena. ,vol. 57, pp. 536- 564 ,(1972) , 10.1016/0031-8914(72)90045-6
S B Shlosman, The method of reflection positivity in the mathematical theory of first-order phase transitions Russian Mathematical Surveys. ,vol. 41, pp. 83- 134 ,(1986) , 10.1070/RM1986V041N03ABEH003322
L. Chayes, J. Machta, GRAPHICAL REPRESENTATIONS AND CLUSTER ALGORITHMS II Physica A-statistical Mechanics and Its Applications. ,vol. 254, pp. 477- 516 ,(1998) , 10.1016/S0378-4371(97)00637-7
Robert G. Edwards, Alan D. Sokal, Generalization of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithm. Physical Review D. ,vol. 38, pp. 2009- 2012 ,(1988) , 10.1103/PHYSREVD.38.2009
Jürg Fröhlich, Robert Israel, Elliot H. Lieb, Barry Simon, Phase transitions and reflection positivity. I. General theory and long range lattice models Communications in Mathematical Physics. ,vol. 62, pp. 1- 34 ,(1978) , 10.1007/BF01940327
Jürg Fröhlich, Elliott H. Lieb, Phase transitions in anisotropic lattice spin systems Communications in Mathematical Physics. ,vol. 60, pp. 233- 267 ,(1978) , 10.1007/978-3-662-10018-9_11
R. Kotecký, S. B. Shlosman, First-order phase transitions in large entropy lattice models Communications in Mathematical Physics. ,vol. 83, pp. 493- 515 ,(1982) , 10.1007/BF01208713
J. Fröhlich, B. Simon, T. Spencer, Infrared Bounds, Phase Transitions and Continuous Symmetry Breaking Communications in Mathematical Physics. ,vol. 50, pp. 79- 95 ,(1976) , 10.1007/BF01608557
L. Chayes, J. Machta, GRAPHICAL REPRESENTATIONS AND CLUSTER ALGORITHMS. I. DISCRETE SPIN SYSTEMS Physica A-statistical Mechanics and Its Applications. ,vol. 239, pp. 542- 601 ,(1997) , 10.1016/S0378-4371(96)00438-4
L. Chayes, R. Kotecky, S. B. Shlosman, Aggregation and intermediate phases in dilute spin systems Communications in Mathematical Physics. ,vol. 171, pp. 203- 232 ,(1995) , 10.1007/BF02103776