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One-dimensional Ising model with long-range interaction

Louis J. Kijewski, M. P. Kawatra

Physics Letters AMay 1, 19706 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

Critical temperature of the one-dimensional Ising model with inverse-square interactions

Anonymous, Abdulai Gassama, Jonah Eick +6 more

Physical review. EOct 2, 20260 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

Finite-range scaling for a one-dimensional system with long-range interactions

Katarina Uzelac, Zvonko Glumac

A procedure, similar to the finite-size scaling, is proposed for systems with long-range interactions. It is applied to the one-dimensional Ising model with interactions decaying as 1/ mod i-j mod 1+ sigma with distance mod i-j mod . The critical temperature and exponent nu are calculated for sigma <or=1.

Journal of Physics A Mathematical and GeneralApr 7, 198819 citations

On the critical temperature of the quasi-one-dimensional Ising model

M. A. Yurishchev

Soviet Journal of Low Temperature PhysicsSep 1, 19880 citations

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

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