World records in the size of simulated Ising models

Stauffer, Dietrich

doi:10.1590/s0103-97332000000400029

Cited by 20 publications

(12 citation statements)

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“…The detailed exploration of the nearcritical behavior is hampered by the necessity of considering systems of very large sizes and, in particular, at d = 4, by the difficulty of an accurate characterization of the slowly varying logarithmic deviations from MF behavior. Moreover, for d 4, the finite-size-scaling theory and the confluent corrections to scaling have been debated [20][21][22][23][24][25]. Thus, relatively few of the numerous available MC studies [17,22,[26][27][28][29][30][31][32][33][34][35] are likely to be extensive enough to yield a satisfactory overall description of these systems at criticality, in spite of the remarkable progress in the simulation algorithms with reduced critical slowdown.…”

Section: Introductionmentioning

confidence: 99%

Triviality problem and high-temperature expansions of higher susceptibilities for the Ising and scalar-field models in four-, five-, and six-dimensional lattices

Butera

Pernici

2012

Phys. Rev. E

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High-temperature expansions are presently the only viable approach to the numerical calculation of the higher susceptibilities for the spin and the scalar-field models on high-dimensional lattices. The critical amplitudes of these quantities enter into a sequence of universal amplitude ratios that determine the critical equation of state. We have obtained a substantial extension, through order 24, of the high-temperature expansions of the free energy (in presence of a magnetic field) for the Ising models with spin s≥1/2 and for the lattice scalar-field theory with quartic self-interaction on the simple-cubic and the body-centered-cubic lattices in four, five, and six spatial dimensions. A numerical analysis of the higher susceptibilities obtained from these expansions yields results consistent with the widely accepted ideas, based on the renormalization group and the constructive approach to Euclidean quantum field theory, concerning the no-interaction ("triviality") property of the continuum (scaling) limit of spin-s Ising and lattice scalar-field models at and above the upper critical dimensionality.

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Section: Introductionmentioning

confidence: 99%

Triviality problem and high-temperature expansions of higher susceptibilities for the Ising and scalar-field models in four-, five-, and six-dimensional lattices

Butera

Pernici

2012

Phys. Rev. E

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“…Thus the real problem is five dimensions, which we discuss now. Figure 5 shows new data for L 5 sites, extending up to L = 201, the largest five-dimensional system known to us from direct simulations (176 5 was simulated in Ising models [12]). They are still compatible with the number of spanning clusters increasing as ln L. These data use MBC's, but similar proportionalities to ln L were found also with free and periodic boundary conditions (PBC's, which means helical boundaries in d − 1 directions), which are illustrated in Fig.…”

Section: Results Of the Simulationsmentioning

confidence: 99%

Number of spanning clusters at the high-dimensional percolation thresholds

et al. 2004

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A scaling theory is used to derive the dependence of the average number k of spanning clusters at threshold on the lattice size L. This number should become independent of L for dimensions d<6 and vary as ln L at d=6 . The predictions for d>6 depend on the boundary conditions, and the results there may vary between L(d-6) and L0. While simulations in six dimensions are consistent with this prediction [after including corrections of order ln(ln L)], in five dimensions the average number of spanning clusters still increases as ln L even up to L=201 . However, the histogram P(k) of the spanning cluster multiplicity does scale as a function of kX(L), with X(L) =1+const/L, indicating that for sufficiently large L the average k will approach a finite value: a fit of the five-dimensional multiplicity data with a constant plus a simple linear correction to scaling reproduces the data very well. Numerical simulations for d>6 and for d=4 are also presented.

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“…These ideas were completely embodied by the Partridge-Barton model [7]. Further studies on this model, have incorporated somatic as well as hereditary mutations [17,18], leaving the model with two mechanisms of senescence: antagonistic pleiotropy and accumulation of bad mutations. But ageing (due to mutations) emerges in these works as a result of turning more intense with age (in some artificial or arbitrary way) the mutational strength.…”

Section: Discussionmentioning

confidence: 99%

Exact solution of an evolutionary model without aging

Onody

Medeiros

1999

Phys. Rev. E

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We introduce an age-structured asexual population model containing all the relevant features of evolutionary ageing theories. Beneficial as well as deleterious mutations, heredity and arbitrary fecundity are present and managed by natural selection. An exact solution without ageing is found. We show that fertility is associated with generalized forms of the Fibonacci sequence, while mutations and natural selection are merged into an integral equation which is solved by Fourier series. Average survival probabilities and Malthusian growth exponents are calculated indicating that the system may exhibit mutational meltdown. The relevance of the model in the context of fissile reproduction groups as many protozoa and coelenterates is discussed.

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World records in the size of simulated Ising models

Cited by 20 publications

References 0 publications

Triviality problem and high-temperature expansions of higher susceptibilities for the Ising and scalar-field models in four-, five-, and six-dimensional lattices

Triviality problem and high-temperature expansions of higher susceptibilities for the Ising and scalar-field models in four-, five-, and six-dimensional lattices

Number of spanning clusters at the high-dimensional percolation thresholds

Exact solution of an evolutionary model without aging

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