An experiment-oriented analysis of 2D spin-glass dynamics: a twelve time-decades scaling study

Abstract

Recent high precision experimental results on spin-glass films ask for a detailed understanding of the domain-growth dynamics of two-dimensional spin glasses. To achieve this goal, we numerically simulate the out-equilibrium dynamics of the Ising spin glass for a time that spans close to twelve orders of magnitude (from picoseconds to order of a second), in systems large enough to avoid finite-size effects. We find that the time-growth of the size of the glassy domains is excellently described by a single scaling function. A single time-scale τ (T ) controls the dynamics. τ (T ) diverges upon approaching the T = 0 critical point. The divergence of τ (T → 0) is Arrhenius-like, with a barrier height that depends very mildly on temperature. The growth of this barrier-height is best described by critical dynamics. As a side product we obtain an impressive confirmation of universality of the equilibrium behavior of two-dimensional spin-glasses. arXiv:1805.06738v4 [cond-mat.dis-nn]

Mean-field phase diagram and spin-glass phase of the dipolar kagome Ising antiferromagnet

“…Yet, the manifestations of the vestige of the transition can be very strong also in two dimensional systems: The spin glass amorphous order can establish over very long (although not infinite) length scales, the spin glass susceptibility can become very large (although not infinite), and the relaxation time can grow very fast at low temperature. Several experimental realizations of two-dimensional spin glasses using thin films do indeed show the same behavior as 3d spin glasses at sufficiently low temperature [53][54][55]. In this sense, the existence of the spin glass phase in higher dimension, accompanied by the growth of long-range amorphous order and a rough free-energy landscape, provides a possible and natural explanation of the slow dynamics observed in the numerical simulations of Ref.…”

Dimensional crossover in the aging dynamics of spin glasses in a film geometry

“…Somewhat surprisingly, we find a rich dynamic behavior with no less than four different regimes (3D growth at short times, a double crossover regime with a faster growth for intermediate times, and a final equilibration regime). We analyze our results by combining the phenomenological Renormalization Group [28] with recent analysis of the two-dimensional spin glass dynamics [16,17]. On the light of our results, the interpretation of thin-film experiments [19][20][21][22] seems essentially correct, albeit slightly oversimplified.…”

“…Before addressing the dimensional crossover, let us recall a few crucial facts about the very different dynamic behavior of spin glasses in spatial dimensions D = 2 [16,17] and D = 3 [15].…”

“…In 2D, we are in the paramagnetic phase for any T > 0. Hence, ξ(t, T ) eventually reaches its equilibrium limit ξ eq (T ), which can be very large [16,32]: for T → 0, ξ eq (T ) ∝ 1/T ν 2D , ν 2D = 3.580(4) [33]. When a 0 ξ(t, T ) ξ eq (T ) we have a power law ξ ∝ t 1/z 2D , with z 2D ≈ 7.14 irrespective of T [16]: 2D dynamics may be much faster than 3D dynamics (aging rates z ∼ 15 are not uncommon in 3D at low T ).…”

“…A possible approach to overcome this difficulty is extracting from the non-equilibrium dynamics crucial information about the (so difficult to reach) equilibrium regime [4][5][6][7]. However, custom-built computers [8] and other simulation advances [9,10] have made it possible to study theoretically [11][12][13][14][15][16][17] the simplest experimental protocol. In this protocol, see e.g.…”