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Ising chain with random short- and long-range interactions

L.L. Gonçalves, André P. Vieira

Journal of Magnetism and Magnetic MaterialsJan 1, 19984 citations

One-dimensional Ising model with long-range interaction

Louis J. Kijewski, M. P. Kawatra

Physics Letters AMay 1, 19706 citations

Critical temperature of one-dimensional Ising model with long-range interaction revisited

José Martínez-Herrera, Omar Abel Rodríguez-López, M. A. Solís

arXiv:2109.14762Physica A Statistical Mechanics and its ApplicationsFeb 25, 20225 citations

Domain statistics in the relaxation of the one-dimensional Ising model with strong long-range interactions

Federico Corberi, Manoj Kumar, Eugenio Lippiello +1 more

arXiv:2303.14715Chaos Solitons & FractalsJul 1, 20238 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

Renormalization-group treatment of the long-ranged one-dimensional Ising model with random fields

P. O. Weir, N. Read, J. Michael Kosterlitz

We construct a renormalization-group theory for a one-dimensional Ising model with longranged interactions and random fields with short-ranged correlations. We find recursion relations near the zero-temperature, finite randomness fixed point, valid for $\ensuremath{\sigma}$ near \textonehalf{}, where the interaction $\frac{J}{(r)}=\frac{J}{{r}^{1+\ensuremath{\sigma}}}$. We also show that the probability distribution for the random fields becomes strongly non-Gaussian under the scaling procedure.We construct a renormalization-group theory for a one-dimensional Ising model with longranged interactions and random fields with short-ranged correlations. We find recursion relations near the zero-temperature, finite randomness fixed point, valid for $\ensuremath{\sigma}$ near \textonehalf{}, where the interaction $\frac{J}{(r)}=\frac{J}{{r}^{1+\ensuremath{\sigma}}}$. We also show that the probability distribution for the random fields becomes strongly non-Gaussian under the scaling procedure.

Physical review. B, Condensed matterOct 1, 19876 citations

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

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