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Dynamical critical exponent of the one-dimensional random transverse-Ising model

Hitoshi Asakawa

Physica A Statistical Mechanics and its ApplicationsNov 1, 19964 citations

Exact bounds for dynamical critical exponents of transverse-field Ising chains with a correlated disorder

Tatsuhiko Shirai, Shu Tanaka

arXiv:2007.07439Annals of PhysicsApr 24, 20214 citations

Short-time critical dynamics for the transverse Ising model

M. Santos

We have analyzed the short-time critical behavior for the one-dimensional quantum transverse Ising model through Monte Carlo simulations at zero temperature. We used the scaling relation for the dynamics at the early time stages in order to obtain the static critical exponents (beta,nu) and the dynamical critical exponent z for this model. While the values found for the static exponents are in agreement with the exact ones, here, the dynamical critical exponent is found for a quantum spin model.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsJun 1, 200014 citations

The critical properties of Ising model with a transverse field

Weitao Song, C. Z. Yang

Solid State CommunicationsJul 1, 19947 citations

Application of a continous time cluster algorithm to the Two-dimensional Random Quantum Ising Ferromagnet

Heiko Rieger, Naoki Kawashima

A cluster algorithm formulated in continuous (imaginary) time is presented for Ising models in a transverse field. It works directly with an infinite number of time-slices in the imaginary time direction, avoiding the necessity to take this limit explicitly. The algorithm is tested at the zero-temperature critical point of the pure two-dimensional (2d) transverse Ising model. Then it is applied to the 2d Ising ferromagnet with random bonds and transverse fields, for which the phase diagram is determined. Finite size scaling at the quantum critical point as well as the study of the quantum Griffiths-McCoy phase indicate that the dynamical critical exponent is infinite as in 1d.A cluster algorithm formulated in continuous (imaginary) time is presented for Ising models in a transverse field. It works directly with an infinite number of time-slices in the imaginary time direction, avoiding the necessity to take this limit explicitly. The algorithm is tested at the zero-temperature critical point of the pure two-dimensional (2d) transverse Ising model. Then it is applied to the 2d Ising ferromagnet with random bonds and transverse fields, for which the phase diagram is determined. Finite size scaling at the quantum critical point as well as the study of the quantum Griffiths-McCoy phase indicate that the dynamical critical exponent is infinite as in 1d.

arXiv:cond-mat/9802104Feb 10, 19981 citation

Quasiparticle dynamics in a quasiperiodic Ising model with temporally fluctuating transverse fields

Kohei Ohgane, Yusuke Masaki, Hiroaki Matsueda

We study quasiparticle dynamics in a quasiperiodic Ising model with temporally fluctuating transverse fields. Specifically, we calculate the dynamical exponents of the standard deviation of a quasiparticle spreading under a field chosen randomly from binary values $\ifmmode\pm\else\textpm\fi{}h$ at every time interval. We find that the short-time behavior of the dynamical exponents depends on the interval of the temporally fluctuating fields. We also reveal how the quasiparticle dynamics affects the relaxation of spin-spin correlation functions. The dynamics can be explained via the overlap between the eigenvectors of a Hamiltonian with $\ifmmode\pm\else\textpm\fi{}h$.We study quasiparticle dynamics in a quasiperiodic Ising model with temporally fluctuating transverse fields. Specifically, we calculate the dynamical exponents of the standard deviation of a quasiparticle spreading under a field chosen randomly from binary values $\ifmmode\pm\else\textpm\fi{}h$ at every time interval. We find that the short-time behavior of the dynamical exponents depends on the interval of the temporally fluctuating fields. We also reveal how the quasiparticle dynamics affects the relaxation of spin-spin correlation functions. The dynamics can be explained via the overlap between the eigenvectors of a Hamiltonian with $\ifmmode\pm\else\textpm\fi{}h$.

Physical review. B./Physical review. BApr 11, 20234 citations

Dynamical Critical Exponents of the Ising Model with a Transverse Field

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