A Theory of Cooperative Phenomena

Kikuchi, Ryoichi

doi:10.1103/physrev.81.988

Cited by 1,886 publications

(826 citation statements)

References 17 publications

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“…The cluster variation method, or CVM for short, is based on a truncation of the cluster (cumulant) expansion of the free energy density functional on which the variational formulation of statistical mechanics is based [12,13]. Unlike mean field theory it generally locates rather accurately the boundaries between different phases in complex phase diagrams and, using the recently proposed cluster variation-Padè approximant method [14,15,16] one can extract non-classical, precise estimates of the critical exponents.…”

Section: The Cluster Variation Methodsmentioning

confidence: 99%

The phase diagram of the gonihedric 3d Ising model via CVM

et al. 1997

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We use the cluster variation method (CVM) to investigate the phase structure of the 3d gonihedric Ising actions defined by Savvidy and Wegner. The geometrical spin cluster boundaries in these systems serve as models for the string worldsheets of the gonihedric string embedded in Z 3 . The models are interesting from the statistical mechanical point of view because they have a vanishing bare surface tension. As a result the action depends only on the angles of the discrete surface and not on the area, which is the antithesis of the standard 3d Ising model.The results obtained with the CVM are in good agreement with Monte Carlo simulations for the critical temperatures and the order of the transition as the selfavoidance coupling κ is varied. The value of the magnetization critical exponent β = 0.062 ± 0.003, calculated with the cluster variation-Padè approximant method, is also close to the simulation results.

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Section: The Cluster Variation Methodsmentioning

confidence: 99%

The phase diagram of the gonihedric 3d Ising model via CVM

et al. 1997

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“…The goal of this paper is to give a detailed study of the model proposed in [1] using the pair approximation of the cluster variation method (CVM) [8], generalized to random systems [9,10]. This approximation improves the standard mean field by taking into account effects of correlation among spins at different sites.…”

Section: Introductionmentioning

confidence: 99%

A cluster variation approach to the random-anisotropy Blume-Emery-Griffiths model

Buzano

Maritan

Pelizzola

1994

J. Phys.: Condens. Matter

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The random-anisotropy Blume-Emery-Griffiths model, which has been proposed to describe the critical behavior of 3 He-4 He mixtures in a porous medium, is studied in the pair approximation of the cluster variation method extended to disordered systems. Several new features, with respect to mean field theory, are found, including a rich ground state, a nonzero percolation threshold, a reentrant coexistence curve and a miscibility gap on the high 3 He concentration side down to zero temperature. Furthermore, nearest neighbor correlations are introduced in the random distribution of the anisotropy, which are shown to be responsible for the raising of the critical temperature with respect to the pure and uncorrelated random cases and contribute to the detachment of the coexistence curve from the λ line.

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“…Manzo and Olivieri [13] used the model to study metastability and nucleation within dynamical MC simulations. Ekiz et al [14] investigated the dynamics of the BC model by using the path probability method (PPM) [15] which is the natural extension into the time dependent of the cluster-variation method (CVM) [16]. In particular, they studied the "flatness" property of metastable states, the "overshooting" phenomenon as well as the role of the unstable state.…”

Section: Introductionmentioning

confidence: 99%

Dynamic phase diagrams of the Blume–Capel model in an oscillating field by the path probability method

Ertaş¹,

Keskín²

2014

Physica A: Statistical Mechanics and its Applications

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We calculate the dynamic phase transition (DPT) temperatures and present the dynamic phase diagrams in the Blume-Capel model under the presence of a time-dependent oscillating external magnetic field by using the path probability method. We study the time variation of the average order parameters to obtain the phases in the system and the paramagnetic (P), ferromagnetic (F) and the F + P mixed phases are found. We also investigate the thermal behavior of the dynamic order parameters to analyze the nature (continuous and discontinuous) of transitions and to obtain the DPT points. We present the dynamic phase diagrams in three planes, namely (T, h), (d, T) and (k 2 /k 1 , T), where T is the reduced temperature, h the reduced magnetic field amplitude, d the reduced crystal-field interaction and the k 2 , k 1 rate constants. The phase diagrams exhibit dynamic tricritical and reentrant behaviors as well as a double critical end point and triple point, strongly depending on the values of the interaction parameters and the rate constants. We compare and discuss the dynamic phase diagrams with dynamic phase diagrams that are obtained within the Glauber-type stochastic dynamics based on the mean-field theory and the effective field theory.

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A Theory of Cooperative Phenomena

Cited by 1,886 publications

References 17 publications

The phase diagram of the gonihedric 3d Ising model via CVM

The phase diagram of the gonihedric 3d Ising model via CVM

A cluster variation approach to the random-anisotropy Blume-Emery-Griffiths model

Dynamic phase diagrams of the Blume–Capel model in an oscillating field by the path probability method

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