Fermi Partition Functions of Friendly Walkers and Pair Connectedness of Directed Percolation : General Physics
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概要
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Non-crossing random walkers with attractive interactions called friendly walkers (FWs) are studied. A restriction on trajectories, which is analogous to Pauli's exclusion principle, is inrposed and the Fermi partition functions are defined. We prove a theorem that the pair connectedness of the bond directed percolation (DP) with bond concentration p is related to the Fermi grand -11(k_B Inp) and the chemical potential partition func,tion of F~V if we set the temperature T = -1/ (k_B1np) and the chemical potential μ= -iπ/1np, where k_B is the Boltzmann constant and i = √<-1>. The pure imaginary chemical potential means that the DP transition can be regarded as a symmetry breaking of parity in the number of FWs. As a corollary of the theorem, a new method is proposed for calculating the series expansion of the pair connectedness and percolation probability of DP using the low-temperature expansion data of FW.
- 社団法人日本物理学会の論文
- 2001-01-15
著者
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Katori Makoto
Department Of Pharmacology Kitasato University School Of Medicine
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INUI Norio
Department of Mechanical and Inteligent Engineering,Himeji Institute of Technology
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KATORI Makoto
Department of Physics,Faculty of Science and Engineering Chuo University
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Inui Norio
Department of Mechanical and Inteligent Engineering, Himiji Institute of Technology
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