We use quantum Monte Carlo methods and various analytic approximations to study the infinite-range Ising spin-glass model in a transverse field in the disordered phase. We focus on the behavior of the frequency dependent susceptibility of the system above and below the critical field. We establish that, at the quantum critical point, there exists an equivalence between the long-time behavior of this model and that of the single-impurity Kondo model. Our predictions for the long-time dynamics of the model are in good agreement with experimental results on ${\mathrm{LiHo}}_{0.167}{\mathrm{Y}}_{0.833}{\mathrm{F}}_{4}$ .We use quantum Monte Carlo methods and various analytic approximations to study the infinite-range Ising spin-glass model in a transverse field in the disordered phase. We focus on the behavior of the frequency dependent susceptibility of the system above and below the critical field. We establish that, at the quantum critical point, there exists an equivalence between the long-time behavior of this model and that of the single-impurity Kondo model. Our predictions for the long-time dynamics of the model are in good agreement with experimental results on ${\mathrm{LiHo}}_{0.167}{\mathrm{Y}}_{0.833}{\mathrm{F}}_{4}$.

arXiv:cond-mat/9802106Physical Review LettersSep 21, 199843 citations

Critical relaxation for spin system with long range interactions

J.M. Winter

Physics Letters AFeb 1, 19732 citations

Correspondence between long-range and short-range spin glasses

R. A. Baños, L. A. Fernández, Víctor Martín-Mayor +1 more

We compare the critical behavior of the short-range Ising spin glass with a spin glass with long-range interactions which fall off as a power $\ensuremath{\sigma}$ of the distance. We show that there is a value of $\ensuremath{\sigma}$ of the long-range model for which the critical behavior is very similar to that of the short-range model in four dimensions. We also study a value of $\ensuremath{\sigma}$ for which we find the critical behavior to be compatible with that of the three-dimensional model, although we have much less precision than in the four-dimensional case.We compare the critical behavior of the short-range Ising spin glass with a spin glass with long-range interactions which fall off as a power $\ensuremath{\sigma}$ of the distance. We show that there is a value of $\ensuremath{\sigma}$ of the long-range model for which the critical behavior is very similar to that of the short-range model in four dimensions. We also study a value of $\ensuremath{\sigma}$ for which we find the critical behavior to be compatible with that of the three-dimensional model, although we have much less precision than in the four-dimensional case.

arXiv:1207.7014Physical Review BOct 17, 201250 citations

Critical dynamics of the spin–boson model

Mikhail Gennag'evich Vasin, S. V. Remizov, Andrey A. Elistratov

arXiv:2501.12457Physica A Statistical Mechanics and its ApplicationsJul 22, 20260 citations

Nonequilibrium Criticality in Quench Dynamics of Long-Range Spin Models

Paraj Titum, Mohammad F. Maghrebi

Long-range interacting spin systems are ubiquitous in physics and exhibit a variety of ground-state disorder-to-order phase transitions. We consider a prototype of infinite-range interacting models known as the Lipkin-Meshkov-Glick model describing the collective interaction of N spins and investigate the dynamical properties of fluctuations and correlations after a sudden quench of the Hamiltonian. Specifically, we focus on critical quenches, where the initial state and/or the postquench Hamiltonian are critical. Depending on the type of quench, we identify three distinct behaviors where both the short-time dynamics and the stationary state at long times are effectively thermal, quantum, and genuinely nonequilibrium, characterized by distinct universality classes and static and dynamical critical exponents. These behaviors can be identified by an infrared effective temperature that is finite, zero, and infinite (the latter scaling with the system size as N^{1/3}), respectively. The quench dynamics is studied through a combination of exact numerics and analytical calculations utilizing the nonequilibrium Keldysh field theory. Our results are amenable to realization in experiments with trapped-ion experiments where long-range interactions naturally arise.Long-range interacting spin systems are ubiquitous in physics and exhibit a variety of ground-state disorder-to-order phase transitions. We consider a prototype of infinite-range interacting models known as the Lipkin-Meshkov-Glick model describing the collective interaction of N spins and investigate the dynamical properties of fluctuations and correlations after a sudden quench of the Hamiltonian. Specifically, we focus on critical quenches, where the initial state and/or the postquench Hamiltonian are critical. Depending on the type of quench, we identify three distinct behaviors where both the short-time dynamics and the stationary state at long times are effectively thermal, quantum, and genuinely nonequilibrium, characterized by distinct universality classes and static and dynamical critical exponents. These behaviors can be identified by an infrared effective temperature that is finite, zero, and infinite (the latter scaling with the system size as N^{1/3}), respectively. The quench dynamics is studied through a combination of exact numerics and analytical calculations utilizing the nonequilibrium Keldysh field theory. Our results are amenable to realization in experiments with trapped-ion experiments where long-range interactions naturally arise.

arXiv:1909.12311Physical Review LettersJul 21, 202025 citations

{\mathrm{LiHo}}_{0.167}{\mathrm{Y}}_{0.833}{\mathrm{F}}_{4}