Exact Solution of an Irreversible One-Dimensional Model with Fully Biased Spin Exchanges

We introduce a model with conserved dynamics, where nearest neighbor pairs of spins ↑↓ (↓↑) can exchange to assume the configuration ↓↑ (↑↓), with rate β(α), through energy decreasing moves only. We report exact solution for the case when one of the rates, α or β, is zero. The irreversibility of such zero-temperature dynamics results in strong dependence on the initial conditions. Domain wall arguments suggest that for more general, finite-temperature models with steady states the dynamical critical exponent for the anisotropic spin exchange is different from the isotropic value.We introduce a model with conserved dynamics, where nearest neighbor pairs of spins ↑↓ (↓↑) can exchange to assume the configuration ↓↑ (↑↓), with rate β(α), through energy decreasing moves only. We report exact solution for the case when one of the rates, α or β, is zero. The irreversibility of such zero-temperature dynamics results in strong dependence on the initial conditions. Domain wall arguments suggest that for more general, finite-temperature models with steady states the dynamical critical exponent for the anisotropic spin exchange is different from the isotropic value.

arXiv:cond-mat/9602122International Journal of Modern Physics BNov 15, 19962 citations

Nonuniversal critical dynamical behavior in 1D spin systems

Eduardo Lage

Recent results concerning non-universality in the dynamical critical behavior of the one-dimensional Ising model, are generalised to several formulations of the Potts model, using arguments based on domain wall motion. By applying real-space renormalisation group methods, the authors also study the dynamical Ising model, with single flips, both for a period distribution of nearest-neighbor exchanges and for the random chain (with nonzero couplings). They show that the critical dynamical exponent is z=1+J M /J m where J M (J m ) is the greatest (smallest) of the exchanges.Recent results concerning non-universality in the dynamical critical behavior of the one-dimensional Ising model, are generalised to several formulations of the Potts model, using arguments based on domain wall motion. By applying real-space renormalisation group methods, the authors also study the dynamical Ising model, with single flips, both for a period distribution of nearest-neighbor exchanges and for the random chain (with nonzero couplings). They show that the critical dynamical exponent is z=1+J M /J m where J M (J m ) is the greatest (smallest) of the exchanges.

Journal of Physics C Solid State PhysicsSep 10, 198714 citations

Critical dynamics of one-dimensional long-range exchange models

Adriana G. Moreira, J. Kamphorst Leal da Silva, F. C. Sá Barreto

One-dimensional kinetic Ising models with long-range exchange of two spins with opposite signs are considered. The exchange probability is a power-law function of the distance between exchanged spins. Rigorous lower bounds for the dynamical exponent z are obtained from the initial response and the scaling hypothesis of the relaxation time. The dependence of the z exponent on the maximal exchange distance and on the exchange probability is studied. Nonuniversal behavior in the ferromagnetic model with two different alternating coupling constants is found. The z exponent is also obtained from the domain-wall argument.One-dimensional kinetic Ising models with long-range exchange of two spins with opposite signs are considered. The exchange probability is a power-law function of the distance between exchanged spins. Rigorous lower bounds for the dynamical exponent z are obtained from the initial response and the scaling hypothesis of the relaxation time. The dependence of the z exponent on the maximal exchange distance and on the exchange probability is studied. Nonuniversal behavior in the ferromagnetic model with two different alternating coupling constants is found. The z exponent is also obtained from the domain-wall argument.

Physical review. B, Condensed matterJul 1, 19932 citations

Exact solution of the biquadratic spin-1 t−J model in one dimension

Francisco Castilho Alcaraz, R. Z. Bariev

A generalization of the $t\ensuremath{-}J$ model with a nearest-neighbor hopping is formulated and solved exactly by the Bethe ansatz method. The model describes the dynamics of spin- $S$ fermions with isotropic or anisotropic interactions. In the case $S=1$ the magnetic interaction is biquadratic in the spin operators. In contrast to the $\mathrm{SU}(N)$ generalization of the $t\ensuremath{-}J$ model, studied previously in the literature, the present model possesses beyond a massless excitation also a massive one. The physical properties indicate the existence of Cooper-type pairs with finite binding energy.A generalization of the $t\ensuremath{-}J$ model with a nearest-neighbor hopping is formulated and solved exactly by the Bethe ansatz method. The model describes the dynamics of spin-$S$ fermions with isotropic or anisotropic interactions. In the case $S=1$ the magnetic interaction is biquadratic in the spin operators. In contrast to the $\mathrm{SU}(N)$ generalization of the $t\ensuremath{-}J$ model, studied previously in the literature, the present model possesses beyond a massless excitation also a massive one. The physical properties indicate the existence of Cooper-type pairs with finite binding energy.

arXiv:cond-mat/9706228Physical review. B, Condensed matterOct 1, 19973 citations

One-dimensional critical dynamics and conservation laws

J. Kamphorst Leal da Silva, F. C. Sá Barreto

The one-dimensional kinetic Ising models with order-parameter conservation are studied for different transition rates. The effect on critical dynamics of global and local conservation laws is considered. Rigorous lower bounds for the dynamical exponent (z) are obtained from the initial response rate and the scaling hypothesis for the relaxation time. It is shown for several dynamical models that z\ensuremath{\ge}5 even if the order-parameter conservation occurs only globally. For models in which the maximal separation between two exchanged spins is proportional to the equilibrium correlation length, the inequality z\ensuremath{\ge}3 is obtained. The d-dimensional case is discussed briefly.The one-dimensional kinetic Ising models with order-parameter conservation are studied for different transition rates. The effect on critical dynamics of global and local conservation laws is considered. Rigorous lower bounds for the dynamical exponent (z) are obtained from the initial response rate and the scaling hypothesis for the relaxation time. It is shown for several dynamical models that z\ensuremath{\ge}5 even if the order-parameter conservation occurs only globally. For models in which the maximal separation between two exchanged spins is proportional to the equilibrium correlation length, the inequality z\ensuremath{\ge}3 is obtained. The d-dimensional case is discussed briefly.

Physical Review AAug 1, 19913 citations

Nonequilibrium current-carrying steady states in the anisotropic XY spin chain

Jarrett L. Lancaster

Out-of-equilibrium behavior is explored in the one-dimensional anisotropic XY model. Initially preparing the system in the isotropic XX model with a linearly varying magnetic field to create a domain-wall magnetization profile, dynamics is generated by rapidly changing the exchange interaction anisotropy and external magnetic field. Relaxation to a nonequilibrium steady state is studied analytically at the critical transverse Ising point, where correlation functions may be computed in closed form. For arbitrary values of anisotropy and external field, an effective generalized Gibbs' ensemble is shown to accurately describe observables in the long-time limit. Additionally, we find spatial oscillations in the exponentially decaying, transverse spin-spin correlation functions with wavelength set by the magnetization jump across the initial domain wall. This wavelength depends only weakly on anisotropy and magnetic field in contrast to the current, which is highly dependent on these parameters.Out-of-equilibrium behavior is explored in the one-dimensional anisotropic XY model. Initially preparing the system in the isotropic XX model with a linearly varying magnetic field to create a domain-wall magnetization profile, dynamics is generated by rapidly changing the exchange interaction anisotropy and external magnetic field. Relaxation to a nonequilibrium steady state is studied analytically at the critical transverse Ising point, where correlation functions may be computed in closed form. For arbitrary values of anisotropy and external field, an effective generalized Gibbs' ensemble is shown to accurately describe observables in the long-time limit. Additionally, we find spatial oscillations in the exponentially decaying, transverse spin-spin correlation functions with wavelength set by the magnetization jump across the initial domain wall. This wavelength depends only weakly on anisotropy and magnetic field in contrast to the current, which is highly dependent on these parameters.

arXiv:1602.08027Physical review. EMay 19, 201623 citations

A generalization of the $t\ensuremath{-}J$ model with a nearest-neighbor hopping is formulated and solved exactly by the Bethe ansatz method. The model describes the dynamics of spin-

S

fermions with isotropic or anisotropic interactions. In the case

S=1

the magnetic interaction is biquadratic in the spin operators. In contrast to the

\mathrm{SU}(N)

generalization of the $t\ensuremath{-}J$ model, studied previously in the literature, the present model possesses beyond a massless excitation also a massive one. The physical properties indicate the existence of Cooper-type pairs with finite binding energy.