High-temperature and strong magnetic field expansions for long range random Ising models

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

Critical temperature and density of spin flips in the anisotropic random-field Ising model

Marc Thilo Figge, MAXIM V. MOSTOVOY, Jasper Knoester

We present analytical results for the strongly anisotropic random-field Ising model, consisting of weakly interacting spin chains. We combine the mean-field treatment of interchain interactions with an analytical calculation of the average chain free energy (``chain mean-field'' approach). The free energy is found using a mapping on a Brownian motion model. We calculate the order parameter and give expressions for the critical random magnetic-field strength below which the ground state exhibits long-range order and for the critical temperature as a function of the random magnetic-field strength. In the limit of vanishing interchain interactions, we obtain corrections to the zero-temperature estimate by Imry and Ma [Phys. Rev. Lett. 35, 1399 (1975)] of the ground-state density of domain walls (spin flips) in the one-dimensional random-field Ising model. One of the problems to which our model has direct relevance is the lattice dimerization in disordered quasi-one-dimensional Peierls materials, such as the conjugated polymer trans-polyacetylene.We present analytical results for the strongly anisotropic random-field Ising model, consisting of weakly interacting spin chains. We combine the mean-field treatment of interchain interactions with an analytical calculation of the average chain free energy (``chain mean-field'' approach). The free energy is found using a mapping on a Brownian motion model. We calculate the order parameter and give expressions for the critical random magnetic-field strength below which the ground state exhibits long-range order and for the critical temperature as a function of the random magnetic-field strength. In the limit of vanishing interchain interactions, we obtain corrections to the zero-temperature estimate by Imry and Ma [Phys. Rev. Lett. 35, 1399 (1975)] of the ground-state density of domain walls (spin flips) in the one-dimensional random-field Ising model. One of the problems to which our model has direct relevance is the lattice dimerization in disordered quasi-one-dimensional Peierls materials, such as the conjugated polymer trans-polyacetylene.

arXiv:cond-mat/9803385Physical review. B, Condensed matterAug 1, 19985 citations

Analysis of a long-range random field quantum antiferromagnetic Ising model

Bikas K. Chakrabarti, Arnab Das, Jun‐ichi Inoue

arXiv:cond-mat/0512043The European Physical Journal BJun 1, 20066 citations

One-dimensional Ising model with long-range and random short-range interactions

A. P. Vieira, L. L. Gonçalves

The one-dimensional Ising model in an external magnetic field with uniform long-range interactions and random short-range interactions satisfying bimodal annealed distributions is studied. This generalizes the random model discussed by Paladin et al. (J. Phys. I France 4, 1994, p. 1597). Exact results are obtained for the thermodynamic functions at arbitrary temperatures, and special attention is given to the induced and spontaneous magnetization. At low temperatures the system can exist in a “ferrimagnetic” phase with magnetization 0 < σ < 1, in addition to the usual paramagnetic, ferromagnetic and antiferromagnetic phases. For a fixed distribution of the random variables the system presents up to three tricritical points for different intensities of the long-range interactions. Field-temperature diagrams can present up to four critical points. 1The one-dimensional Ising model in an external magnetic field with uniform long-range interactions and random short-range interactions satisfying bimodal annealed distributions is studied. This generalizes the random model discussed by Paladin et al. (J. Phys. I France 4, 1994, p. 1597). Exact results are obtained for the thermodynamic functions at arbitrary temperatures, and special attention is given to the induced and spontaneous magnetization. At low temperatures the system can exist in a “ferrimagnetic” phase with magnetization 0 < σ < 1, in addition to the usual paramagnetic, ferromagnetic and antiferromagnetic phases. For a fixed distribution of the random variables the system presents up to three tricritical points for different intensities of the long-range interactions. Field-temperature diagrams can present up to four critical points. 1

Jan 1, 20084 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.