The behavior of the nonlinear susceptibility ${\ensuremath{\chi}}_{3}$ and its relation to the spin-glass transition temperature ${T}_{f}$ in the presence of random fields are investigated. To accomplish this task, the Sherrington-Kirkpatrick model is studied through the replica formalism, within a one-step replica-symmetry-breaking procedure. In addition, the dependence of the Almeida-Thouless eigenvalue ${\ensuremath{\lambda}}_{\mathrm{AT}}$ (replicon) on the random fields is analyzed. Particularly, in the absence of random fields, the temperature ${T}_{f}$ can be traced by a divergence in the spin-glass susceptibility ${\ensuremath{\chi}}_{\mathrm{SG}}$, which presents a term inversely proportional to the replicon ${\ensuremath{\lambda}}_{\mathrm{AT}}$. As a result of a relation between ${\ensuremath{\chi}}_{\mathrm{SG}}$ and ${\ensuremath{\chi}}_{3}$, the latter also presents a divergence at ${T}_{f}$ , which comes as a direct consequence of ${\ensuremath{\lambda}}_{\mathrm{AT}}=0$ at ${T}_{f}$ . However, our results show that, in the presence of random fields, ${\ensuremath{\chi}}_{3}$ presents a rounded maximum at a temperature ${T}^{*}$ which does not coincide with the spin-glass transition temperature ${T}_{f}$ (i.e., ${T}^{*}>{T}_{f}$ for a given applied random field). Thus, the maximum value of ${\ensuremath{\chi}}_{3}$ at ${T}^{*}$ reflects the effects of the random fields in the paramagnetic phase instead of the nontrivial ergodicity breaking associated with the spin-glass phase transition. It is also shown that ${\ensuremath{\chi}}_{3}$ still maintains a dependence on the replicon ${\ensuremath{\lambda}}_{\mathrm{AT}}$, although in a more complicated way as compared with the case without random fields. These results are discussed in view of recent observations in the ${\mathrm{LiHo}}_{x}{\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{F}}_{4}$ compound.The behavior of the nonlinear susceptibility ${\ensuremath{\chi}}_{3}$ and its relation to the spin-glass transition temperature ${T}_{f}$ in the presence of random fields are investigated. To accomplish this task, the Sherrington-Kirkpatrick model is studied through the replica formalism, within a one-step replica-symmetry-breaking procedure. In addition, the dependence of the Almeida-Thouless eigenvalue ${\ensuremath{\lambda}}_{\mathrm{AT}}$ (replicon) on the random fields is analyzed. Particularly, in the absence of random fields, the temperature ${T}_{f}$ can be traced by a divergence in the spin-glass susceptibility ${\ensuremath{\chi}}_{\mathrm{SG}}$, which presents a term inversely proportional to the replicon ${\ensuremath{\lambda}}_{\mathrm{AT}}$. As a result of a relation between ${\ensuremath{\chi}}_{\mathrm{SG}}$ and ${\ensuremath{\chi}}_{3}$, the latter also presents a divergence at ${T}_{f}$, which comes as a direct consequence of ${\ensuremath{\lambda}}_{\mathrm{AT}}=0$ at ${T}_{f}$. However, our results show that, in the presence of random fields, ${\ensuremath{\chi}}_{3}$ presents a rounded maximum at a temperature ${T}^{*}$ which does not coincide with the spin-glass transition temperature ${T}_{f}$ (i.e., ${T}^{*}>{T}_{f}$ for a given applied random field). Thus, the maximum value of ${\ensuremath{\chi}}_{3}$ at ${T}^{*}$ reflects the effects of the random fields in the paramagnetic phase instead of the nontrivial ergodicity breaking associated with the spin-glass phase transition. It is also shown that ${\ensuremath{\chi}}_{3}$ still maintains a dependence on the replicon ${\ensuremath{\lambda}}_{\mathrm{AT}}$, although in a more complicated way as compared with the case without random fields. These results are discussed in view of recent observations in the ${\mathrm{LiHo}}_{x}{\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{F}}_{4}$ compound.

arXiv:1606.01186Physical review. B./Physical review. BJun 17, 20167 citations

Dynamical phase transitions and spin glasses

Bernard Derrida

Physics ReportsDec 1, 198927 citations

Studies of the phase diagram of randomly interacting fermionic systems

Oppermann, R., Bernd Rosenow

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.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.

arXiv:cond-mat/9803249Mar 20, 19980 citations

Quantum phase transition in spin glasses with multi-spin interactions

Theo M. Nieuwenhuizen, Félix Ritort

arXiv:cond-mat/9706244Physica A Statistical Mechanics and its ApplicationsFeb 1, 199850 citations

Ising spin glass in a transverse field: Replica-symmetry-breaking solution

Yadin Y. Goldschmidt, Pik-Yin Lai

The replica-symmetry-breaking (RSB) solution of the infinite-range Ising spin glass in the presence of a transverse field is obtained. The quenched free energy and the phase boundary of the glass transition temperature versus the transverse field are calculated at first-step RSB without using the static approximation. We demonstrate that replica symmetry (RS) has to be broken in the spin-glass phase by comparing the free energies of the RSB and RS solutions. No evidence is found to support an intermediate spin-glass phase with replica symmetry.The replica-symmetry-breaking (RSB) solution of the infinite-range Ising spin glass in the presence of a transverse field is obtained. The quenched free energy and the phase boundary of the glass transition temperature versus the transverse field are calculated at first-step RSB without using the static approximation. We demonstrate that replica symmetry (RS) has to be broken in the spin-glass phase by comparing the free energies of the RSB and RS solutions. No evidence is found to support an intermediate spin-glass phase with replica symmetry.

Physical Review LettersMay 21, 1990117 citations

The behavior of the nonlinear susceptibility ${\ensuremath{\chi}}_{3}$ and its relation to the spin-glass transition temperature

{T}_{f}

in the presence of random fields are investigated. To accomplish this task, the Sherrington-Kirkpatrick model is studied through the replica formalism, within a one-step replica-symmetry-breaking procedure. In addition, the dependence of the Almeida-Thouless eigenvalue ${\ensuremath{\lambda}}_{\mathrm{AT}}$ (replicon) on the random fields is analyzed. Particularly, in the absence of random fields, the temperature

{T}_{f}

can be traced by a divergence in the spin-glass susceptibility ${\ensuremath{\chi}}_{\mathrm{SG}}$, which presents a term inversely proportional to the replicon ${\ensuremath{\lambda}}_{\mathrm{AT}}$. As a result of a relation between ${\ensuremath{\chi}}_{\mathrm{SG}}$ and ${\ensuremath{\chi}}_{3}$, the latter also presents a divergence at

{T}_{f}

, which comes as a direct consequence of ${\ensuremath{\lambda}}_{\mathrm{AT}}=0$ at

{T}_{f}

. However, our results show that, in the presence of random fields, ${\ensuremath{\chi}}_{3}$ presents a rounded maximum at a temperature

{T}^{*}

which does not coincide with the spin-glass transition temperature

{T}_{f}

(i.e.,

{T}^{*}>{T}_{f}

for a given applied random field). Thus, the maximum value of ${\ensuremath{\chi}}_{3}$ at

{T}^{*}

reflects the effects of the random fields in the paramagnetic phase instead of the nontrivial ergodicity breaking associated with the spin-glass phase transition. It is also shown that ${\ensuremath{\chi}}_{3}$ still maintains a dependence on the replicon ${\ensuremath{\lambda}}_{\mathrm{AT}}$, although in a more complicated way as compared with the case without random fields. These results are discussed in view of recent observations in the ${\mathrm{LiHo}}_{x}{\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{F}}_{4}$ compound.