Studies of the phase diagram of randomly interacting fermionic systems

TL;DR

This paper explores the complex phase diagrams of fermionic systems with random interactions, highlighting the role of chemical potential, phase transitions, and replica symmetry breaking in spin glass models and their quantum extensions.

Contribution

It provides a detailed analysis of phase transitions in fermionic spin glasses, including the effects of chemical potential and quantum dynamics, extending classical models to fermionic systems.

Findings

Spin glass order decays discontinuously beyond a critical chemical potential.

Quantum paramagnet to spin glass transition remains replica-symmetric at T=0.

RPSB influences the phase diagram at zero temperature.

Abstract

We present details of the phase diagrams of fermionic systems with random and frustrated interactions, emphasizing the important role of the chemical potential. The insulating fermionic Ising spin glass model is shown to reveal different entangled magnetic instabilities and phase transitions. We review tricritical phenomena related to the strong correspondence between charge and spin fluctuations, being controlled by quantum statistics. We compare the spin density diluted Sherrington-Kirkpatrick spin glass with classical spin 1 models such as the BEG model. We analyse in detail the infinite range model and show that spin glass order must decay discontinuously as the chemical potential exceeds a critical value, provided the temperature is below the tricritical one, and that the T=0 transition is of classical type. Parisi replica permutation symmetry breaking (RPSB) governs the thermal spin glass transitions and fermionic modifications of the SK-models AT-line emerge. RPSB takes place everywhere within the fermionic spin glass phase. Although the critical field theory of the quantum paramagnet to spin glass transition in metallic systems remains replica--symmetric at T=0, with only small corrections at low T from RPSB, the phase diagram is affected at O(T^0) by RPSB. Generalizing our results for the fermionic Ising spin glass we consider aspects of models with additional spin and charge quantum--dynamics such as metallic spin glasses.