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Effects of geometry on transfer matrices, spin chains and critical behaviour
Author(s) -
Davies Brian,
Peschel Ingo
Publication year - 1993
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19935050107
Subject(s) - eigenvalues and eigenvectors , critical point (mathematics) , ising model , physics , bounded function , transfer matrix , spectrum (functional analysis) , spin (aerodynamics) , transfer (computing) , critical phenomena , transfer matrix method (optics) , quantum , point (geometry) , condensed matter physics , quantum mechanics , geometry , mathematical analysis , mathematics , phase transition , parallel computing , computer science , computer vision , thermodynamics
We consider two‐dimensional Ising models bounded by general parabolic curves and study their transfer matrices and associated quantum spin chains. We derive their eigenvalue spectra numerically and analytically, both at the critical point and in its vicinity. From this we find how the geometrical form of the system is reflected in the spectrum and how it influences the critical behaviour near the tip.