Spin-s Spin-Glass Phases in the d=3 Ising Model

TL;DR

This study uses renormalization-group theory to analyze higher-spin Ising spin glasses in three dimensions, revealing a persistent finite-temperature spin-glass phase with chaotic behavior across all spin values.

Contribution

It demonstrates that a finite-temperature spin-glass phase exists for all spin values in d=3 and characterizes its chaotic properties and phase diagram saturation.

Findings

Finite-temperature spin-glass phase for all s in d=3

Chaotic behavior with Lyapunov exponent 1.93

Phase diagram saturation as s increases

Abstract

All higher-spin s >= 1/2 Ising spin glasses are studied by renormalization-group theory in spatial dimension d=3. 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 \rightarrow \infty. 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 behaviors. The ferromagnetic-spinglass-antiferromagnetic phase transitions occurring around p_t = 0.37 and 0.63 are unaffected by s, confirming the percolative nature of this phase transition.