Out-of-equilibrium 2D Ising spin glass: almost, but not quite, a free-field theory

Abstract

We consider the spatial correlation function of the two-dimensional Ising spin glass under out-equilibrium conditions. We pay special attention to the scaling limit reached upon approaching zero temperature. The field-theory of a non-interacting field makes a surprisingly good job at describing the spatial shape of the correlation function of the out-equilibrium Edwards-Anderson Ising model in two dimensions. arXiv:1805.08504v2 [cond-mat.dis-nn]

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

“…(7)]. While C eq 4 (r) decays exponentially in r, C 4 (r, t w ) decays super-exponentially C 4 (r, t w ) ∼ e −(r/ξ) β , with β > 1 [25]. Note that the time C 4 (r, t w ) needs to coalesce with C eq 4 (r) depends strongly on r.…”

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].…”

“…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.…”

“…In this protocol, see e.g. [18], a spin glass at some very high-temperature is fastly quenched to the working temperature T < T c and the excruciatingly slow growth of the spin-glass correlation length ξ is afterwards studied as a function of the time elapsed since the quench, t. Although simulations do not approach yet the experimental time and length scales (t ∼ 1 hour and ξ ∼ 100 a 0 , where a 0 is the average distance between magnetic moments), the range covered is already significant: from picoseconds to milliseconds [9,10] or even 0.1 seconds using dedicated computers [11,15] (or conventional ones in the case of twodimensional spin glasses [16,17]).…”