Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
29 (1988), S. 2280-2287
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
Three theorems dealing with transfer matrices in statistical mechanical systems are proved. The theorems state that the nonzero eigenvalues of transfer matrices formed through various prescriptions are identical. Hence it is possible to ascribe a physical meaning to all the eigenvalues of a transfer matrix, not just to the few largest eigenvalues. The first theorem states that the transfer matrix formed by building a system M layers at a time has as its only nonzero eigenvalues the eigenvalues of the transfer matrix formed by building the M layers of the system one at a time. This theorem relates the product of two nM×nM M-layer transfer matrices to the product of M one-layer M×M transfer matrices. The second theorem states that one of the nM×nM M-layer transfer matrices (for M〉1) has only one nonzero eigenvalue. A procedure for finding this eigenvalue and all eigenvectors is given. The third theorem generalizes the first to the case where the chosen layering is not an integer multiple of the interaction length.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.528108
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