Overfrustrated and Underfrustrated Spin-Glasses in d=3 and 2: Evolution of Phase Diagrams and Chaos Including Spin-Glass Order in d=2

Abstract

In spin-glass systems, frustration can be adjusted continuously and considerably, without changing the antiferromagnetic bond probability p, by using locally correlated quenched randomness, as we demonstrate here on hypercubic lattices and hierarchical lattices. Such overfrustrated and underfrustrated Ising systems on hierarchical lattices in d=3 and 2 are studied. With the removal of just 51 % of frustration, a spin-glass phase occurs in d=2. With the addition of just 33 % frustration, the spin-glass phase disappears in d=3. Sequences of 18 different phase diagrams for different levels of frustration are calculated in both dimensions. In general, frustration lowers the spin-glass ordering temperature. At low temperatures, increased frustration favors the spin-glass phase (before it disappears) over the ferromagnetic phase and symmetrically the antiferromagnetic phase. When any amount, including infinitesimal, frustration is introduced, the chaotic rescaling of local interactions occurs in the spin-glass phase. Chaos increases with increasing frustration, as seen from the increased positive value of the calculated Lyapunov exponent $\lambda$, starting from $\lambda =0$ when frustration is absent. The calculated runaway exponent $y_R$ of the renormalization-group flows decreases with increasing frustration to $y_R=0$ when the spin-glass phase disappears. From our calculations of entropy and specific heat curves in d=3, it is seen that frustration lowers in temperature the onset of both long- and short-range order in spin-glass phases, but is more effective on the former. From calculations of the entropy as a function of antiferromagnetic bond concentration p, it is seen that the ground-state and low-temperature entropy already mostly sets in within the ferromagnetic and antiferromagnetic phases, before the spin-glass phase is reached.

Published version, 18 phase diagrams, 12 figures, 10 pages

References in corpus (16)

• Temperature and Disorder Chaos in Three-Dimensional Ising Spin Glasses
• Contrasting the magnetic response between magnetic-glass and reentrant spin-glass
• Temperature chaos in 3D Ising Spin Glasses is driven by rare events
• Random subcubes as a toy model for constraint satisfaction problems
• Disorder chaos in spin glasses
• Free energy fluctuations and chaos in the Sherrington-Kirkpatrick model
• High q-State Clock Spin Glasses in Three Dimensions and the Lyapunov Exponents of Chaotic Phases and Chaotic Phase Boundaries
• Multicritical Point Relations in Three Dual Pairs of Hierarchical-Lattice Ising Spin-Glasses
• Reentrant and Forward Phase Diagrams of the Anisotropic Three-Dimensional Ising Spin Glass
• Temperature Chaos in Two-Dimensional Ising Spin Glasses with Binary Couplings: a Further Case for Universality
• Bond chaos in the Sherrington-Kirkpatrick model
• On temperature chaos in Ising and XY Spin Glasses
• Zeros of the Potts Model Partition Function on Sierpinski Graphs
• Quenched-Vacancy Induced Spin-Glass Order
• A percolation model with continuously varying exponents
• Chaotic Spin Correlations in Frustrated Ising Hierarchical Lattices

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