Low Temperature Linear Dynamical Susceptibility of the Ising Spin Glass in a Transverse Field

Abstract

Low-temperature equilibrium dynamical behavior of the linear ac susceptibility in d-dimensional Ising spin glass with short-range interactions between spins in transverse field is investigated in terms of droplet model. The real part of linear ac susceptibility [Formula: see text] as functions of temperature T and frequency of external ac field ω is calculated. Frequency and temperature dependence of [Formula: see text] shows a glassy behavior. For instance, we find a broad maximum for [Formula: see text] which shifts towards higher temperatures with increasing frequency of ac-field. The temperature of maximum Tf(ω) depends on frequency and increases with frequency up to the magnitude where [Formula: see text] starts to decrease. A qualitative agreement of our calculations with experimental data, for example, in quantum dipole magnet LiHoxY1-xF4 and proton glasses, is found.

Out-of-Equilibrium Dissipative <i>ac</i>—Susceptibility in Quantum Ising Spin Glass

“…The droplet model describing the low-dimensional shortrange Ising spin glass is based on renormalization group arguments [26,28]. In dimensions above the lower critical dimension l (usually in spin glass l ) the droplet model finds a low temperature spin-glass phase in zero magnetic field.…”

“…In this paper we use a phenomenological quantum droplet model of spin glass theory [26][27][28][29] (which does not use the mean-field approximation) in order to describe the non equilibrium behavior of the magnetic dynamical susceptibility at very low (but finite) temperatures .…”

“…and mixed betaine phosphate-phosphite [28]. The transverse field in [28] is interpreted as the frequency of the proton tunneling.…”

Low temperature nonequilibrium dynamics in transverse Ising spin glass

“…The natural basis for the interpretation of aging is based on coarsening ideas of a slow domain growth of a spin-glass type ordered phase [6,9,15]. For theoretical studies of quantum fluctuations in disordered media there is a variety of techniques including replica theory, renormalization group, Monte Carlo simulations, the Schwinger and Keldysh closed-time path-integral formalism and others [26][27][28][29][30][31][32][33][34][35][36][37][38]. A large attention in the last decade was payed to the spin glasses representing a model systems for study of nonequilibrium dynamics [39][40][41][42][43][44][45][46][47].…”

Dynamic nonlinear (cubic) susceptibility in quantum Ising spin glass

“…A basic assumption of the droplet picture is that the spin glass dynamics is governed by large-scale excitations whose relaxation time increases with length scale. In previous papers [16] we have calculated the real and imaginary parts of linear dynamic susceptibility in the same model, as in [6], for very low nonzero temperatures using the general linear response theory of magnetic dispersion and absorption phenomena for quantum systems by Kubo and Tomita [17]. We note that in [6] the real part of the cubic nonlinear ac susceptibility was defined as the in-phase 3ω magnetization response M(3ω) to a small time-dependent applied field h cos(ωt)…”