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Solid State Communications

Freezing of the extended states in mean field theory of dilute Ising spin glasses with long range interactions

Boris E. Vugmeister, Dan W. Nowakowski, David L. Huber

Published Dec 1, 1995• 9 citations
Publisher
DOI
10.1016/0038-1098(95)00424-6

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The spin-glass transition in a magnetic field is studied both in and out of the limit of validity of mean-field theory on a diluted one dimensional chain of Ising spins where exchange bonds occur with a probability decaying as the inverse power of the distance. Varying the power in this long-range model corresponds, in a one-to-one relationship, to changing the dimension in spin-glass short-range models. Evidence for a spin-glass transition in a magnetic field is found also for systems whose equivalent dimension is below the upper critical dimension in a zero magnetic field.

arXiv:0811.3435•Physical Review Letters•Dec 22, 2009•79 citations
The onset of spin glass freezing in dilute Ising systems with long range interactions is investigated within the framework of a random local field approach (previously developed for disordered ferromagnets and ferroelectrics) with the use of numerical simulations. The problem reduces to the diagonalization of an N×N random matrix, N being the number of spins in the simulation, whose elements depend on the spin–spin interaction and temperature. We identify the onset of spin glass freezing with the temperature at which this boundary eigenvalue separating localized and extended states is equal to one. Numerical simulations give a reasonable value of the freezing temperature for dilute RKKY spin glasses and reproduce its linear concentration dependence in agreement with the scaling relation.
Inverse freezing is analyzed in a cluster spin-glass (SG) model that considers infinite-range disordered interactions between magnetic moments of different clusters (intercluster interaction) and short-range antiferromagnetic coupling J(1) between Ising spins of the same cluster (intracluster interaction). The intercluster disorder J is treated within a mean-field theory by using a framework of one-step replica symmetry breaking. The effective model obtained by this treatment is computed by means of an exact diagonalization method. With the results we build phase diagrams of temperature T/J versus J(1)/J for several sizes of clusters n(s) (number of spins in the cluster). The phase diagrams show a second-order transition from the paramagnetic phase to the SG order at the freezing temperature T(f) when J(1)/J is small. The increase in J(1)/J can then destroy the SG phase. It decreases T(f)/J and introduces a first-order transition. In addition, inverse freezing can arise at a certain range of J(1)/J and large enough n(s). Therefore, the nontrivial frustration generated by disorder and short-range antiferromagnetic coupling can introduce inverse freezing spontaneously.
The spin-glass transition in a magnetic field is studied both in and out of the limit of validity of mean-field theory on a diluted one dimensional chain of Ising spins where exchange bonds occur with a probability decaying as the inverse power of the distance. Varying the power in this long-range model corresponds, in a one-to-one relationship, to changing the dimension in spin-glass short-range models. Evidence for a spin-glass transition in a magnetic field is found also for systems whose equivalent dimension is below the upper critical dimension in a zero magnetic field.