Geodesic
Two-dimensional four-line models of the~Ising model type
Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 2, pp. 281-298

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We briefly describe the theory of root transfer matrices for four-line models with the field in the new indexless form. We use theoretical and numerical methods to reveal new effects in the theory of singular points and phase transitions. A substantial part of the results is obtained using a numerical algorithm that drastically {(}at least exponentially{\rm)} reduces the computational complexity of Ising-type models by using the extremely sparse root transfer matrix.
Keywords: Ising model, partition function, free energy, magnetization, magnetic susceptibility, critical point, singular curve
Mots-clés : transfer matrix, ferromagnet, antiferromagnet, phase transition. 
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     author = {V. V. Katrakhov and Yu. N. Kharchenko},
     title = {Two-dimensional four-line models of {the~Ising} model type},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {281--298},
     publisher = {mathdoc},
     volume = {149},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_149_2_a8/}
}
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V. V. Katrakhov; Yu. N. Kharchenko. Two-dimensional four-line models of the~Ising model type. Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 2, pp. 281-298. http://geodesic.mathdoc.fr/item/TMF_2006_149_2_a8/