Universality in the time correlations of the long-range 1d Ising model

被引：15

作者：

Corberi, Federico ^{[1
,2
,3
]}

Lippiello, Eugenio ^{[4
]}

Politi, Paolo ^{[5
,6
]}

机构：

[1] Univ Salerno, Dipartimento Fis ER Caianiello, Via Giovanni Paolo II 132, I-84084 Fisciano, SA, Italy

[2] Univ Salerno, Ist Nazl Fis Nucl, Grp Collegato Salerno, Via Giovanni Paolo II 132, I-84084 Fisciano, SA, Italy

[3] Univ Salerno, CNISM, Unita Salerno, Via Giovanni Paolo II 132, I-84084 Fisciano, SA, Italy

[4] Univ Campania L Vanvitelli, Dipartimento Matemat & Fis, Viale Lincoln 5, I-81100 Caserta, Italy

[5] CNR, Ist Sistemi Complessi, Via Madonna Piano 10, I-50019 Sesto Fiorentino, Italy

[6] Ist Nazl Fis Nucl, Sez Firenze, Via G Sansone 1, I-50019 Sesto Fiorentino, Italy

来源：

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT | 2019年

关键词：

correlation functions; kinetic Ising models; numerical simulations; coarsening processes; PHASE-TRANSITION; GROWTH; DECAY;

D O I：

10.1088/1742-5468/ab270a

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

The equilibrium and nonequilibrium properties of ferromagnetic systems may be affected by the long-range nature of the coupling interaction. Here we study the phase separation process of a one-dimensional Ising model in the presence of a power-law decaying coupling, J(r) = 1/r(1+sigma) with sigma > 0, and we focus on the two-time autocorrelation function C(t, t(w)) = < s(i)(t)s(i)(t(w))>. We find that it obeys the scaling form C(t, t(w)) = f (L(t(w))/L(t)), where L(t) is the typical domain size at time t, and where f (x) can only be of two types. For sigma > 1, when domain walls diffuse freely, f (x) falls in the nearest-neighbour (nn) universality class. Conversely, for sigma <= 1, when domain walls dynamics is driven, f (x) displays a new universal behavior. In particular, the so-called Fisher-Huse exponent, which characterizes the asymptotic behavior of f (x) similar or equal to x(-lambda) for x >> 1, is lambda = 1 in the nn universality class (sigma > 1) and lambda = 1/2 for sigma <= 1.

引用

页数：10