Distribution of interevent avalanche times in disordered and frustrated spin systems

Abstract

Hysteresis loops and the associated avalanche statistics of spin systems, such as the random-field Ising and Edwards-Anderson spin-glass models, have been extensively studied. A particular focus has been on selforganized criticality, manifest in power-law distributions of avalanche sizes. Considerably less work has been done on the statistics of the times between avalanches. This paper considers this issue, generalizing the work of Nampoothiri et al. [Phys. Rev. E 96, 032107 (2017)] in one space dimension to higher space dimensions. In addition to the interevent statistics of all avalanches, we also consider what happens when events are restricted to those exceeding a certain threshold size. Doing so raises the possibility of altering the definition of time to count the number of small events between the large ones, which provides for an analog to the concept of natural time introduced by the geophysics community with the goal of predicting patterns in seismic events. We analyze the distribution of time and natural time intervals both in the case of models that include only nearest-neighbor interactions, as well as models with (sparse) long-range couplings. PACS numbers: 75.50.Lk, 75.40.Mg, 05.50.+q arXiv:1808.10497v2 [cond-mat.dis-nn]

Estimating the Epicenter of a Future Strong Earthquake in Southern California, Mexico, and Central America by Means of Natural Time Analysis and Earthquake Nowcasting

“…Natural time was introduced [ 5 ] in 2001 as a general method to analyze time-series resulting from complex systems [ 7 ]. It has been applied to a variety of fields, such as condensed matter physics [ 22 , 23 , 24 ], geophysics [ 6 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 ], civil engineering [ 35 , 36 , 37 , 38 ], climatology [ 39 , 40 , 41 , 42 ], and biomedical engineering [ 43 , 44 ]. Within the concept of NTA, it has been shown that the variance of natural time may be considered as an order parameter for seismicity [ 3 , 45 , 46 , 47 , 48 , 49 ] as well as in acoustic emission before fracture [ 28 , 50 ] or in other self-organized critical phenomena such as ricepiles [ 51 ] and avalanches in the Olami–Feder–Christensen [ 52 ] earthquake model [ 53 ] or in the Burridge–Knopoff [ 54 ] train model [ 55 ].…”

Natural Time Analysis of Global Seismicity

“…The applications of NTA that have appeared up to 2010 have been reviewed in the monograph by Varotsos et al [4], providing examples in various disciplines such as Statistical Physics, Condended Matter Physics, Geophysics, Seismology, Biology, and Cardiology. Since 2011, various newer applications have appeared in a variety of scientific fields, such as condensed matter and materials [17][18][19], geosciences [20][21][22][23][24][25][26][27][28], engineering [29][30][31][32][33][34][35][36], climate change [37][38][39][40], and cosmic rays [41]. Earthquake nowcasting introduced by Rundle et al [42], which is the most recent method for seismic risk estimation by means of the earthquake potential score (EPS), is also based on the concept of natural time.…”