Partition-function zeros of spherical spin glasses and their relevance to chaos

Abstract

We investigate partition-function zeros of the many-body interacting spherical spin glass, the so-called $p$-spin spherical model, with respect to the complex temperature in the thermodynamic limit. We use the replica method and extend the procedure of the replica symmetry breaking ansatz to be applicable in the complex-parameter case. We derive the phase diagrams in the complex-temperature plane and calculate the density of zeros in each phase. Near the imaginary axis away from the origin, there is a replica symmetric phase having a large density. On the other hand, we observe no density in the spin-glass phases, irrespective of the replica symmetry breaking. We speculate that this suggests the absence of the temperature chaos. To confirm this, we investigate the multiple many-body interacting case which is known to exhibit the chaos effect. The result shows that the density of zeros actually takes finite values in the spin-glass phase, even on the real axis. These observations indicate that the density of zeros is more closely connected to the chaos effect than the replica symmetry breaking.

22 pages, 8 figures

References in corpus (6)

• Nature of the spin-glass phase at experimental length scales
• Temperature and Disorder Chaos in Three-Dimensional Ising Spin Glasses
• Behavior of Ising Spin Glasses in a Magnetic Field
• Distribution of Lee-Yang zeros and Griffiths singularities in the $\pm J$ model of spin glasses
• Replica symmetry breaking, complexity and spin representation in the generalized random energy model
• Statistical mechanics of Monte Carlo sampling and the sign problem

Cited by in corpus (6)

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• Dynamical Singularities of Glassy Systems in a Quantum Quench
• Complex Random Energy Model: Zeros and Fluctuations
• Zeros of the partition function and dynamical singularities in spin-glass systems
• Fisher zeroes and the fluctuations of the spectral form factor of chaotic systems
• Analytic continuation over complex landscapes