Self-Induced Glassiness and Pattern Formation in Spin Systems Subject to Long-Range Interactions

Principi, Alessandro; Katsnelson, M. I.

doi:10.1103/physrevlett.117.137201

Cited by 14 publications

(22 citation statements)

References 50 publications

(102 reference statements)

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“…For α= 2.5, the Q-histogram is characterized by four peaks, at non-zero Q values, each along either the negative/positive Q x or Q y axis. The corresponding picture in real space, as illustrated in in figure 3, is that there are many low lying metastable states with no clear long-range ordered pattern, similar to previously observed self-induced glasses [22,23]. Therefore, we identify this regime as the SQG regime.…”

Section: Q-space and Energy Histograms As Regime Identifierssupporting

confidence: 63%

“…Here, we propose that an ordered and finite 2D array of Ising spins interacting via a well-defined long-range RKKY interaction [21] can be used to create energy landscapes with a tunable level of complexity. By changing the ratio α=λ/a between the RKKY wavelength (λ) and the lattice constant (a), the energy landscape of the spin array can be tuned between three different magnetic regimes, ranging from a regime with double-well potential (DW), through a multi-well potential (MW) regime, to a spin glass-like regime, similar to what has been previously studied in [22,23]. We refer to this regime as a spin-Q glass (SQG) (figure 1) [24].…”

Section: Introductionmentioning

confidence: 89%

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Atom-by-atom construction of attractors in a tunable finite size spin array

et al. 2020

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We demonstrate that a two-dimensional finite and periodic array of Ising spins coupled via RKKY-like exchange can exhibit tunable magnetic states ranging across three distinct magnetic regimes: (1) a conventional ferromagnetic regime, (2) a glass-like regime, and (3) a new multi-well regime. These magnetic regimes can be tuned by one gate-like parameter, namely the ratio between the lattice constant and the oscillating interaction wavelength. We characterize the various magnetic regimes, quantifying the distribution of low energy states, aging relaxation dynamics, and scaling behavior. The glassy and multi-well behavior results from the competing character of the oscillating long-range exchange interactions with respect to the lattice. The multi-well structure features multiple attractors, each with a sizable basin of attraction. This may open the possible application of such atomic arrays as associative memories.

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Section: Q-space and Energy Histograms As Regime Identifierssupporting

confidence: 63%

Section: Introductionmentioning

confidence: 89%

Atom-by-atom construction of attractors in a tunable finite size spin array

et al. 2020

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“…Certain types of competing interactions result in the formation of glassy states as captured in the concept of self-induced glassiness ( 60 – 62 ). For example, for magnetic stripe domains, quasi-chaotic patterns result from competition between short-range but strong exchange interaction which tend to maximize magnetization, both locally and globally, and long-range but weak dipole–dipole interaction requiring that the total magnetization of the system be equal to zero ( 61 ).…”

Section: Glasses Patterns Frustrated States and Socmentioning

confidence: 99%

“…One of the formal criteria of the glass state is “universal flexibility” ( 68 ). Because this is the criterion used in the theory of self-induced glassiness ( 60 – 62 ) that is directly relevant for the present analysis, it merits a brief description. Consider a configuration (of spins, atomic positions, dipolar moments, or other parameters) that is characterized by a function

, where x is a d- dimensional vector characterizing a position in space (in most physical applications, d = 2 or 3).…”

Section: Glasses Patterns Frustrated States and Socmentioning

confidence: 99%

Physical foundations of biological complexity

Wolf

Katsnelson

Koonin

2018

Proc. Natl. Acad. Sci. U.S.A.

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109

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SignificanceLiving organisms are characterized by a degree of hierarchical complexity that appears to be inaccessible to even the most complex inanimate objects. Routes and patterns of the evolution of complexity are poorly understood. We propose a general conceptual framework for emergence of complexity through competing interactions and frustrated states similar to those that yield patterns in striped glasses and cause self-organized criticality. We show that biological evolution is replete with competing interactions and frustration that, in particular, drive major transitions in evolution. The key distinction between biological and nonbiological systems seems to be the existence of long-term digital memory and phenotype-to-genotype feedback in living matter.

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“…The original glass concept was developed for disordered systems with some type of randomness in the interatomic interactions. Actually, such randomness is not essential as clearly demonstrated in the concept of self-induced glassiness [65][66][67]. It turns out that some systems satisfy the criterion of Eq.…”

Section: Life Glasses and Patterns: Frustrated Systems And Biologicamentioning

confidence: 99%

Towards physical principles of biological evolution

Katsnelson¹,

Wolf

Koonin

2017

Preprint

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Biological systems reach organizational complexity that far exceeds the complexity of any known inanimate objects. Biological entities undoubtedly obey the laws of quantum physics and statistical mechanics. However, is modern physics sufficient to adequately describe, model and explain the evolution of biological complexity? Detailed parallels have been drawn between statistical thermodynamics and the population-genetic theory of biological evolution. Based on these parallels, we outline new perspectives on biological innovation and major transitions in evolution, and introduce a biological equivalent of thermodynamic potential that reflects the innovation propensity of an evolving population. Deep analogies have been suggested to also exist between the properties of biological entities and processes, and those of frustrated states in physics, such as glasses. Such systems are characterized by frustration whereby local state with minimal free energy conflict with the global minimum, resulting in "emergent phenomena". We extend such analogies by examining frustration-type phenomena, such as conflicts between different levels of selection, in biological evolution. These frustration effects appear to drive the evolution of biological complexity. We further address evolution in multidimensional fitness landscapes from the point of view of percolation theory and suggest that percolation at level above the critical threshold dictates the tree-like evolution of complex organisms. Taken together, these multiple connections between fundamental processes in physics and biology imply that construction of a meaningful physical theory of biological evolution might not be a futile effort. However, it is unrealistic to expect that such a theory can be created in one scoop;if it ever comes to being, this can only happen through integration of multiple physical models of evolutionary processes. Furthermore, the existing framework of theoretical physics is unlikely to suffice for adequate modeling of the biological level of complexity, and new developments within physics itself are likely to be required.

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Self-Induced Glassiness and Pattern Formation in Spin Systems Subject to Long-Range Interactions

Cited by 14 publications

References 50 publications

Atom-by-atom construction of attractors in a tunable finite size spin array

Atom-by-atom construction of attractors in a tunable finite size spin array

Physical foundations of biological complexity

Towards physical principles of biological evolution

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