Theoretical and Mathematical Physics

Cluster expansion and spectrum of the transfer matrix of the two-dimensional ising model with strong external field

Pavel Khrapov

Published Jul 1, 1984• 0 citations

Publisher

DOI: 10.1007/bf01018259

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Theoretical and Mathematical Physics

Cluster expansion and spectrum of the transfer matrix of the two-dimensional ising model with strong external field

Pavel Khrapov

Published Jul 1, 1984• 0 citations

Publisher

DOI: 10.1007/bf01018259

Related papers

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P. N. Bibikov

arXiv:2109.10446Journal of Statistical Mechanics Theory and ExperimentFeb 1, 20220 citations

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David Evans, John T. Lewis

Communications in Mathematical PhysicsSep 1, 19846 citations

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Sh. S. Mamatov

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Two-dimensional Ising model in random magnetic fields

I. Morgenstern, Kurt Binder, Richard M. Hornreich

The statistical mechanics of finite $L\ifmmode\times\else\texttimes\fi{}L$ Ising square lattices in a field $\ifmmode\pm\else\textpm\fi{}h$ of random sign is investigated numerically by a modified recursive transfer matrix method for $6<~L<~16$ . Our results are consistent with the absence of a spontaneous magnetization for $h\ensuremath{\ne}0$ even in the ground state. The singularities occurring at $T=0$ in the range $0<~h<~4J$ , $J$ being the exchange constant, are discussed in terms of a cluster expansion. For nonzero $T$ , less than the critical temperature of the pure two-dimensional Ising model, and $h$ sufficiently small, the system exhibits a nonzero spin-glass order parameter of the Mattis type although there is no magnetization. The ferromagnetic correlation function becomes long ranged for $h\ensuremath{\rightarrow}0$ and is calculated from the domain-wall density.The statistical mechanics of finite $L\ifmmode\times\else\texttimes\fi{}L$ Ising square lattices in a field $\ifmmode\pm\else\textpm\fi{}h$ of random sign is investigated numerically by a modified recursive transfer matrix method for $6<~L<~16$. Our results are consistent with the absence of a spontaneous magnetization for $h\ensuremath{\ne}0$ even in the ground state. The singularities occurring at $T=0$ in the range $0<~h<~4J$, $J$ being the exchange constant, are discussed in terms of a cluster expansion. For nonzero $T$, less than the critical temperature of the pure two-dimensional Ising model, and $h$ sufficiently small, the system exhibits a nonzero spin-glass order parameter of the Mattis type although there is no magnetization. The ferromagnetic correlation function becomes long ranged for $h\ensuremath{\rightarrow}0$ and is calculated from the domain-wall density.

Physical review. B, Condensed matterJan 1, 198197 citations

6<~L<~16

. Our results are consistent with the absence of a spontaneous magnetization for $h\ensuremath{\ne}0$ even in the ground state. The singularities occurring at

T=0

in the range

0<~h<~4J

J

being the exchange constant, are discussed in terms of a cluster expansion. For nonzero

T

, less than the critical temperature of the pure two-dimensional Ising model, and

h

sufficiently small, the system exhibits a nonzero spin-glass order parameter of the Mattis type although there is no magnetization. The ferromagnetic correlation function becomes long ranged for $h\ensuremath{\rightarrow}0$ and is calculated from the domain-wall density.