Monte Carlo study of the Yukawa coupled two-spin Ising model

Brower, Richard C.; Orginos, Kostas; Shen, Yue; Tan, C-I

doi:10.1016/0378-4371(95)00261-5

Cited by 2 publications

(1 citation statement)

References 11 publications

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“…When K = 0, the system reduces to two uncoupled Ising models, having a phase transition at the Onsager critical point (βJ [42,43], β being the inverse temperature. This critical point is shifted by the presence of a finite interlayer coupling K. The resulting Ising critical line separating the paramagnetic and ferromagnetic phases as a function of K has been studied in the literature [44][45][46]. It is clear that the bilayer system (4) is the classical counterpart of two coupled quantum Ising chains in a transverse field, a system that has been studied both in relation to its spectrum, phase transitions and possibility to determine an integrable line in the space of parameters [47][48][49][50].…”

Section: Multi-layer Ising Modelsmentioning

confidence: 99%

Detecting composite orders in layered models via machine learning

Rzadkowski,

Defenu,

Chiacchiera

et al. 2019

Preprint

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We use machine learning to study layered spin models where composite order parameters may emerge as a consequence of the interlayerer coupling. We focus on the layered Ising and Ashkin-Teller models, determining their phase diagram via the application of a machine learning algorithm to the Monte Carlo data. Remarkably our technique is able to correctly characterize all the system phases also in the case of hidden order parameters, i.e. order parameters whose expression in terms of the microscopic configurations would require additional preprocessing of the data fed to the algorithm. Within the approach we introduce, owing to the construction of convolutional neural networks, naturally suitable for layered image-like data with arbitrary number of layers, no preprocessing of the Monte Carlo data is needed, also with regard to its spatial structure. The physical meaning of our results is discussed and compared with analytical data, where available. Yet, the method can be used without any a priori knowledge of the phases one seeks to find.

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Section: Multi-layer Ising Modelsmentioning

confidence: 99%

Detecting composite orders in layered models via machine learning

Rzadkowski,

Defenu,

Chiacchiera

et al. 2019

Preprint

View full text Add to dashboard Cite

show abstract

Detecting composite orders in layered models via machine learning

et al. 2020

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Determining the phase diagram of systems consisting of smaller subsystems ‘connected’ via a tunable coupling is a challenging task relevant for a variety of physical settings. A general question is whether new phases, not present in the uncoupled limit, may arise. We use machine learning and a suitable quasidistance between different points of the phase diagram to study layered spin models, in which the spin variables constituting each of the uncoupled systems (to which we refer as layers) are coupled to each other via an interlayer coupling. In such systems, in general, composite order parameters involving spins of different layers may emerge as a consequence of the interlayer coupling. We focus on the layered Ising and Ashkin–Teller models as a paradigmatic case study, determining their phase diagram via the application of a machine learning algorithm to the Monte Carlo data. Remarkably our technique is able to correctly characterize all the system phases also in the case of hidden order parameters, i.e. order parameters whose expression in terms of the microscopic configurations would require additional preprocessing of the data fed to the algorithm. We correctly retrieve the three known phases of the Ashkin–Teller model with ferromagnetic couplings, including the phase described by a composite order parameter. For the bilayer and trilayer Ising models the phases we find are only the ferromagnetic and the paramagnetic ones. Within the approach we introduce, owing to the construction of convolutional neural networks, naturally suitable for layered image-like data with arbitrary number of layers, no preprocessing of the Monte Carlo data is needed, also with regard to its spatial structure. The physical meaning of our results is discussed and compared with analytical data, where available. Yet, the method can be used without any a priori knowledge of the phases one seeks to find and can be applied to other models and structures.

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Monte Carlo study of the Yukawa coupled two-spin Ising model

Cited by 2 publications

References 11 publications

Detecting composite orders in layered models via machine learning

Detecting composite orders in layered models via machine learning

Detecting composite orders in layered models via machine learning

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