Finite-size scaling of the Glauber model of critical dynamics

Luscombe, James H.; Luban, Marshall; Reynolds, Joseph P.

doi:10.1103/physreve.53.5852

Cited by 46 publications

(39 citation statements)

References 9 publications

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“…Y is a real, symmetric, tridiagonal, N × N matrix, with nonzero a-dimensional eigenvalues λ j (j = 1, ..., N ), while Φ (λj ) are the corresponding N ×1 eigenvectors. In the limiting case h 0 → 0, the numerical solutions for λ j coincide with the ones obtained 21,22 in the framework of a finite-size scaling calculation of the Glauber dynamics in a zero static field. In particular, the low-temperature expansion (k B We are interested in the long time behavior of the system, characterized for being independent on the initial condition.…”

Section: B Finite Chainsupporting

confidence: 75%

“…Therefore we are faced with the theoretical problem of determining how the kinetic equations of motion for the time-dependent spin averages of a finite, open chain in zero magnetic field 21,22 are modified by the presence of magnetic field of the general form (11) i.e. the sum of a static dc field of any intensity, H dc , and of an ac field, oscillating at the angular frequency ω.…”

Section: Dynamic Propertiesmentioning

confidence: 99%

“…21,22,29 As in the case of the infinite chain, we can introduce the local-equilibrium approximation 29,30 in order to truncate the infinite sequence of equations for the higher-order time-dependent spin correlation function. Next we perform the linearization of the kinetic equations, in the hypothesis of a linear response to the ac magnetic field.…”

Section: B Finite Chainmentioning

confidence: 99%

“…so that the dynamic susceptibility, χ(ω), is (22) where χ ∞ denotes the static susceptibility of the infinite Ising chain for H dc = 0…”

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confidence: 99%

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Finite-size effects on the dynamic susceptibility of CoPhOMe single-chain molecular magnets in presence of a static magnetic field

et al. 2011

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The static and dynamic properties of the single-chain molecular magnet [Co(hfac)2NITPhOMe] are investigated in the framework of the Ising model with Glauber dynamics, in order to take into account both the effect of an applied magnetic field and a finite size of the chains. For static fields of moderate intensity and short chain lengths, the approximation of a mono-exponential decay of the magnetization fluctuations is found to be valid at low temperatures; for strong fields and long chains, a multi-exponential decay should rather be assumed. The effect of an oscillating magnetic field, with intensity much smaller than that of the static one, is included in the theory in order to obtain the dynamic susceptibility χ(ω). We find that, for an open chain with N spins, χ(ω) can be written as a weighted sum of N frequency contributions, with a sum rule relating the frequency weights to the static susceptibility of the chain. Very good agreement is found between the theoretical dynamic susceptibility and the ac susceptibility measured in moderate static fields (H dc ≤ 2 kOe), where the approximation of a single dominating frequency turns out to be valid. For static fields in this range, new data for the relaxation time, τ versus H dc , of the magnetization of CoPhOMe at low temperature are also well reproduced by theory, provided that finite-size effects are included.

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Section: B Finite Chainsupporting

confidence: 75%

Section: Dynamic Propertiesmentioning

confidence: 99%

Section: B Finite Chainmentioning

confidence: 99%

“…so that the dynamic susceptibility, χ(ω), is (22) where χ ∞ denotes the static susceptibility of the infinite Ising chain for H dc = 0…”

mentioning

confidence: 99%

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Finite-size effects on the dynamic susceptibility of CoPhOMe single-chain molecular magnets in presence of a static magnetic field

et al. 2011

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“…Finite-size scaling of the Glauber model has been discussed [12,13]. In the case of open chains of size L, a crossover on the relaxation time has been predicted when the magnetic correlation length of the infinite chain, ξ, becomes of the order of L :…”

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confidence: 99%

Glauber dynamics in a single-chain magnet: From theory to real systems

et al. 2004

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The Glauber dynamics is studied in a single-chain magnet (SCM). As predicted a single relaxation mode of the magnetization is found. Above 2.7 K, the thermally activated relaxation time is mainly governed by the effect of magnetic correlations and the energy barrier experienced by each magnetic unit. This result is in perfect agreement with independent thermodynamical measurements. Below 2.7 K, a crossover towards a relaxation regime is observed that is interpreted as the manifestation of finite-size effects. The temperature dependences of the relaxation time and of the magnetic susceptibility reveal the importance of the boundary conditions. PACS numbers: 75.10. Pq, 75.40.Gb, 76.90.+d The design of new slow-relaxing magnetic nanosystems is a very challenging goal for both applications (as information storage) and fundamental research. A wellknown example of such systems is the single-molecule magnet (SMM) that shows slow reversal of the magnetization due to the combined effect of a high spin ground state and uniaxial anisotropy producing an energy barrier between spin-up and spin-down states [1]. When a magnetic field is initially applied to magnetize this system and then removed, the magnetization decays with a material-inherent relaxation time depending on the temperature. The corresponding relaxation time, τ , follows an Arrhenius law at high temperatures and the activation energy is equal to the barrier height, being roughly |D|S 2 , where D is the negative uniaxial anisotropy constant and S is the spin ground state of the molecule. At lower temperatures, τ may saturate when quantum tunneling through the barrier becomes relevant [2].Another research route of metastable magnetism has recently been explored with the synthesis of single-chain magnets (SCMs) [3,4,5]. In these materials, the slow relaxation of magnetization is not solely the consequence of the uniaxial anisotropy seen by each spin on the chain but depends also on magnetic correlations. The effect of the short-range order becomes more and more important when the temperature is reduced until a critical point is reached at T = 0 K for 1D systems. In fact, the relaxation time is found to be exponentially enhanced at low temperatures in agreement with the pioneer work of R. J. Glauber devoted to the dynamics of the 1D Ising model [6]. Although it seems that there is a reasonable agreement between the experimental data and the Glauber's theory [3,4,5], we show in this communication that several other arguments should be considered to fill the gap between the theory and the experimental results. Firstly, it should be mentioned that the experimental sys- tems are not strictly Ising-like. In the simplest case, they are rather described by an anisotropic Heisenberg model:where J is the ferromagnetic exchange constant between the spin units and D is the single-ion anisotropy. Secondly, the relaxation time of each magnetic unit, introduced phenomenologically in Glauber's study, is a priori temperature dependent [7] and this argument should also be consid...

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