The effect of a discrete distribution of annealed random fields on the properties of the two-dimensional Ising model is studied. The random field is allowed to assume the values 0,\ifmmode\pm\else\textpm\fi{}h with the probabilities ${p}_{0}$ ,${p}_{\ifmmode\pm\else\textpm\fi{}}$, and a parameter \ensuremath{\mu} is introduced which is determined by specifying ${p}_{0}$ . Exact results are obtained by mapping the model onto an effective Ising model on the rectangular lattice without field, and the probabilities ${p}_{0}$ ,${p}_{\ifmmode\pm\else\textpm\fi{}}$ are expressed in terms of the magnetization and two-spin correlations of the effective model. It is shown that the long-range order is not destroyed by the random field and the transition temperature increases as ${p}_{0}$ decreases. For a given ${p}_{0}$ the critical temperature increases with the field strength and these combined effects show that the annealed random field favors the ordering of the system, therefore presenting behavior opposite to that expected for the system in a quenched random field.The effect of a discrete distribution of annealed random fields on the properties of the two-dimensional Ising model is studied. The random field is allowed to assume the values 0,\ifmmode\pm\else\textpm\fi{}h with the probabilities ${p}_{0}$,${p}_{\ifmmode\pm\else\textpm\fi{}}$, and a parameter \ensuremath{\mu} is introduced which is determined by specifying ${p}_{0}$. Exact results are obtained by mapping the model onto an effective Ising model on the rectangular lattice without field, and the probabilities ${p}_{0}$,${p}_{\ifmmode\pm\else\textpm\fi{}}$ are expressed in terms of the magnetization and two-spin correlations of the effective model. It is shown that the long-range order is not destroyed by the random field and the transition temperature increases as ${p}_{0}$ decreases. For a given ${p}_{0}$ the critical temperature increases with the field strength and these combined effects show that the annealed random field favors the ordering of the system, therefore presenting behavior opposite to that expected for the system in a quenched random field.

Physical review. B, Condensed matterApr 1, 19863 citations

Critical phenomena of random and quantum spin systems

Hidetsugu Kitatani, 北谷英嗣

Jan 1, 19990 citations

Localization transition induced by programmable disorder

Jaime L. C. da C. Filho, Zoe Gonzalez Izquierdo, A. Saguia +3 more

We investigate the occurrence of many-body localization (MBL) on a spin-1/2 transverse-field Ising model defined on a Chimera connectivity graph with random exchange interactions and longitudinal fields. We observe a transition from an ergodic phase to a nonthermal phase for individual energy eigenstates induced by a critical disorder strength for the Ising parameters. Our result follows from the analysis of both the mean half-system block entanglement and the energy-level statistics. We identify the critical point associated with this transition using the maximum variance of the block entanglement over the disorder ensemble as a function of the disorder strength. The calculated energy density phase diagram shows the existence of a mobility edge in the energy spectrum. In terms of the energy-level statistics, the system changes from the Gaussian orthogonal ensemble for weak disorder to a Poisson distribution limit for strong randomness, which implies localization behavior. We then realize the time-independent disordered Ising Hamiltonian experimentally using a reverse annealing quench-pause-quench protocol on a $\mathrm{D}$ -wave 2000Q programmable quantum annealer. We characterize the transition from the thermal to the localized phase through magnetization measurements at the end of the annealing dynamics, and the results are compatible with our theoretical prediction for the critical point. However, the same behavior can be reproduced using a classical spin-vector Monte Carlo simulation, which suggests that genuine quantum signatures of the phase transition remain out of reach using this experimental platform and protocol.We investigate the occurrence of many-body localization (MBL) on a spin-1/2 transverse-field Ising model defined on a Chimera connectivity graph with random exchange interactions and longitudinal fields. We observe a transition from an ergodic phase to a nonthermal phase for individual energy eigenstates induced by a critical disorder strength for the Ising parameters. Our result follows from the analysis of both the mean half-system block entanglement and the energy-level statistics. We identify the critical point associated with this transition using the maximum variance of the block entanglement over the disorder ensemble as a function of the disorder strength. The calculated energy density phase diagram shows the existence of a mobility edge in the energy spectrum. In terms of the energy-level statistics, the system changes from the Gaussian orthogonal ensemble for weak disorder to a Poisson distribution limit for strong randomness, which implies localization behavior. We then realize the time-independent disordered Ising Hamiltonian experimentally using a reverse annealing quench-pause-quench protocol on a $\mathrm{D}$-wave 2000Q programmable quantum annealer. We characterize the transition from the thermal to the localized phase through magnetization measurements at the end of the annealing dynamics, and the results are compatible with our theoretical prediction for the critical point. However, the same behavior can be reproduced using a classical spin-vector Monte Carlo simulation, which suggests that genuine quantum signatures of the phase transition remain out of reach using this experimental platform and protocol.

arXiv:2108.06762Physical review. B./Physical review. BApr 1, 20228 citations

Critical temperature of mixed ferromagnetic and antiferromagnetic Ising systems with arbitrary spin

J Jakubczak, Z. Mrozińska, Andrzej Pękalski

Using the high-temperature series expansion method, a system of randomly mixed ferromagnetic and antiferromagnetic Ising bonds is considered in quenched and annealed systems for an arbitrary value of spin and a BCC lattice. The dependence of the critical temperature on the concentration p of ferromagnetic bonds is determined. It is found that the resulting phase diagrams depend on the system (whether quenched or annealed), the spin value and the strength of the coupling constants. Also the dependence of the critical exponent gamma on p and the crossover exponent phi are estimated.Using the high-temperature series expansion method, a system of randomly mixed ferromagnetic and antiferromagnetic Ising bonds is considered in quenched and annealed systems for an arbitrary value of spin and a BCC lattice. The dependence of the critical temperature on the concentration p of ferromagnetic bonds is determined. It is found that the resulting phase diagrams depend on the system (whether quenched or annealed), the spin value and the strength of the coupling constants. Also the dependence of the critical exponent gamma on p and the crossover exponent phi are estimated.

Journal of Physics C Solid State PhysicsJun 28, 19795 citations

{p}_{0}

,${p}_{\ifmmode\pm\else\textpm\fi{}}$, and a parameter \ensuremath{\mu} is introduced which is determined by specifying

{p}_{0}

. Exact results are obtained by mapping the model onto an effective Ising model on the rectangular lattice without field, and the probabilities

{p}_{0}

,${p}_{\ifmmode\pm\else\textpm\fi{}}$ are expressed in terms of the magnetization and two-spin correlations of the effective model. It is shown that the long-range order is not destroyed by the random field and the transition temperature increases as

{p}_{0}

decreases. For a given

{p}_{0}

the critical temperature increases with the field strength and these combined effects show that the annealed random field favors the ordering of the system, therefore presenting behavior opposite to that expected for the system in a quenched random field.

\mathrm{D}

-wave 2000Q programmable quantum annealer. We characterize the transition from the thermal to the localized phase through magnetization measurements at the end of the annealing dynamics, and the results are compatible with our theoretical prediction for the critical point. However, the same behavior can be reproduced using a classical spin-vector Monte Carlo simulation, which suggests that genuine quantum signatures of the phase transition remain out of reach using this experimental platform and protocol.