On the statistics of binary alloys in one-dimensional quasiperiodic lattices

Бадалян, Д. А.; Gasparian, V.; Khachatrian, A.Gh.; Ortuño, M.; Ruiz, J.; Cuevas, E.

doi:10.1016/0921-4526(95)00536-6

Cited by 2 publications

(1 citation statement)

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“…This is the main difficulty of the transfer matrices method and arose in many studies in the theory of 1D disordered systems and particularly of calculation of partition function in 1D disordered magnetic Ising systems in the intermediate region, i.e., when the magnetic field (or temperature) is not very high or low (see, e.g., Refs. 5, 6). The situation becomes more complicated when we deal with two or more random parameters as in the case of 1D Ising inhomogeneous model with random magnetic field at each site in addition to nearest‐neighbor random exchange integrals.…”

Section: Introductionmentioning

confidence: 99%

One‐dimensional disordered magnetic Ising systems: A new approach

Gasparian

Бадалян

Jódar

2009

Physica Status Solidi (b)

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We reconsider the problem of a one‐dimensional Ising model with an arbitrary nearest‐neighbor random exchange integral, temperature, and random magnetic field in each site. A convenient formalism is developed that reduces the partition function to a recurrence equation, which is convenient both for numerical as well as for analytical approaches. We have calculated asymptotic expressions for an ensemble averaged free energy and the averaged magnetization in the case of strong and weak couplings in external constant magnetic field. With a random magnetic field at each site in addition to nearest‐neighbor random exchange integrals we also evaluated the free energy. We show that the zeros of the partition function for the Ising model in the complex external magnetic field plane formally coincide with the singularities of the real part of electron's transmission amplitude through the chain of δ‐function potentials.

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Section: Introductionmentioning

confidence: 99%