Spin-s spin-glass phases in the d=3 Ising model

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Date

2021

Authors

Berker, A. Nihat

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Amer Physical Soc

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Abstract

All higher-spin (s >= 1/2) Ising spin glasses are studied by renormalization-group theory in spatial dimension d = 3, exactly on a d = 3 hierarchical model and, simultaneously, by the Migdal-Kadanoff approximation on the cubic lattice. The s-sequence of global phase diagrams, the chaos Lyapunov exponent, and the spin-glass runaway exponent are calculated. It is found that, in d = 3, a finite-temperature spin-glass phase occurs for all spin values, including the continuum limit of s -> infinity. The phase diagrams, with increasing spin s, saturate to a limit value. The spin-glass phase, for all s, exhibits chaotic behavior under rescalings, with the calculated Lyapunov exponent of lambda = 1.93 and runaway exponent of y(R) = 0.24, showing simultaneous strong-chaos and strong-coupling behavior. The ferromagnetic-spin-glass and spin-glass-antiferromagnetic phase transitions occurring, along their whole length, respectively at p(t) = 0.37 and 0.63 are unaffected by s, confirming the percolative nature of this phase transition.

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Lower Critical Dimension, High-Temperature Series, Renormalization-Group, Hierarchical Lattices, Confluent Singularities, Systems, Transitions, Susceptibility, Expansions, 1st-Order, Lower Critical Dimension, High-Temperature Series, Renormalization-Group, Hierarchical Lattices, Confluent Singularities, Systems, Transitions, Susceptibility, Expansions, 1st-Order

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1

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Physical Review E

Volume

104

Issue

4

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