Low-temperature renormalization group for ferromagnets with long-range interactions

Sak, J.

doi:10.1103/physrevb.15.4344

Cited by 72 publications

(68 citation statements)

References 11 publications

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“…It is well-known that long range interactions between spins can affect the critical behavior of magnets. If we consider the addition of a term r,r ′ V (r − r ′ )s(r)s(r ′ ) to an Ising Hamiltonian, where V (r) ∼ r −(d+σ) corresponds to a long range interaction decaying as a power law, a crossover to long range behavior is obtained provided that σ < 2 − η sr , where η sr is the value of the critical exponent η for short range force [39][40][41]. A similar behavior has also been reported in percolation phenomena with long range correlations [42].…”

Section: Discussionmentioning

confidence: 99%

Fracture model with variable range of interaction

et al. 2002

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We introduce a fiber bundle model where the interaction among fibers is modeled by an adjustable stress-transfer function which can interpolate between the two limiting cases of load redistribution, the global and the local load sharing schemes. By varying the range of interaction several features of the model are numerically studied and a crossover from mean field to short range behavior is obtained. The properties of the two regimes and the emergence of the crossover in between are explored by numerically studying the dependence of the ultimate strength of the material on the system size, the distribution of avalanches of breakings, and of the cluster sizes of broken fibers. Finally, we analyze the moments of the cluster size distributions to accurately determine the value at which the crossover is observed..

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Section: Discussionmentioning

confidence: 99%

Fracture model with variable range of interaction

et al. 2002

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“…Later it was pointed out, in the cases of (4 − ǫ) dimensions [19] and in (2 + ǫ) dimensions [25] that the crossover from LR to SR critical behavior is shifted and occurs at a "critical" value of σ given by σ c = 2 − η(2). As a result η = η(σ) is a continuous function in σ at σ = 2, since η(σ c ) = η(2).…”

Section: Basic Results In the Bulk Casementioning

confidence: 99%

“…These results were generalized to the O(n) vector ϕ 4 model by means of perturbation theory in combination with the renormalization group (RG) technique near the upper critical dimension [18,19,20,21,22,23] d = 2σ, lower critical dimension [24,25,26] d = σ, and the 1/n-expansion [27,28]. Computer simulations also contributed to the exploration of the critical properties of such systems [29,30,31,32,33,34,35].…”

Section: Basic Results In the Bulk Casementioning

confidence: 99%

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Critical Behavior of Systems With Long-Range Interaction in Restricted Geometry

Chamati

Tonchev

2003

Mod. Phys. Lett. B

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The present review is devoted to the problems of finite-size scaling due to the presence of longrange interaction decaying at large distance as 1/r d+σ , σ > 0. The attention is focused mainly on the renormalization group results in the framework of O(n) ϕ 4 -theory for systems with fully finite (block) geometry under periodic boundary conditions. Some bulk critical properties and Monte Carlo results also are reviewed. The role of the cutoff effects as well their relation with those originating from the long-range interaction is also discussed. Special attention is paid to the description of the adequate mathematical technique that allows to treat the long-range and short-range interactions on equal ground. The review closes with short discussion of some open problems. * Electronic address: chamati@issp.bas.bg † Electronic address: tonchev@issp.bas.bg

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“…The contributions χ ∞ and χ st do not depend on the single-cluster critical behavior. Integrating the singlecluster susceptibility over all dynamic clusters using (43) yields (at p = p c )…”

Section: Beyond the Large-n Limit: Scaling Approachmentioning

confidence: 99%

Percolation transition in quantum Ising and rotor models with sub-Ohmic dissipation

2012

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We investigate the influence of sub-Ohmic dissipation on randomly diluted quantum Ising and rotor models. The dissipation causes the quantum dynamics of sufficiently large percolation clusters to freeze completely. As a result, the zero-temperature quantum phase transition across the lattice percolation threshold separates an unusual super-paramagnetic cluster phase from an inhomogeneous ferromagnetic phase. We determine the lowtemperature thermodynamic behavior in both phases, which is dominated by large frozen and slowly fluctuating percolation clusters. We relate our results to the smeared transition scenario for disordered quantum phase transitions, and we compare the cases of sub-Ohmic, Ohmic, and super-Ohmic dissipation.

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Low-temperature renormalization group for ferromagnets with long-range interactions

Cited by 72 publications

References 11 publications

Fracture model with variable range of interaction

Fracture model with variable range of interaction

Critical Behavior of Systems With Long-Range Interaction in Restricted Geometry

Percolation transition in quantum Ising and rotor models with sub-Ohmic dissipation

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