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  • Ising model  (5)
  • Springer  (5)
  • American Institute of Physics (AIP)
  • Periodicals Archive Online (PAO)
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Keywords
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  • Springer  (5)
  • American Institute of Physics (AIP)
  • Periodicals Archive Online (PAO)
Years
  • 1
    Electronic Resource
    Electronic Resource
    On the ferromagnetic Ising model in noninteger spatial dimension (1982)
    Springer
    Journal of statistical physics 29 (1982), S. 699-716 
    Details
    ISSN: 1572-9613
    Keywords: Ising model ; Yang-Lee theorem ; dimensional analytic continuation ; series expansions methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Using the necessary and sufficient conditions in terms of the high-field series coefficients that the Yang-Lee theorem holds, we prove rigorously by counterexample that it cannot be extended to general noninteger dimension, when such models are defined by the “natural” analytic continuation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01011786
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A Markov-property Monte Carlo method: One-dimensional Ising model (1993)
    Springer
    Journal of statistical physics 72 (1993), S. 621-641 
    Details
    ISSN: 1572-9613
    Keywords: Monte Carlo ; Markov property ; Ising model ; critical phenomena
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper we introduce a new Monte Carlo procedure based on the Markov property. This procedure is particularly well suited to massively parallel computation. We illustrate the method on the critical phenomena of the well known one-dimensional Ising model. In the course of this work we found that the autocorrelation time for the Metropolis Monte Carlo algorithm is closely given by the square of the correlation length. We find speedup factors of the order of 1 million for the method as implemented on the CM2 relative to a serial machine. Our procedure gives error estimates which are quite consistent with the observed deviations from the analytically known exact results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01048026
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  • 3
    Electronic Resource
    Electronic Resource
    The border model in one dimension (1990)
    Springer
    Journal of statistical physics 58 (1990), S. 467-474 
    Details
    ISSN: 1572-9613
    Keywords: Ising model ; border model ; Padé approximants ; series analysis ; universality ; pluralism ; field theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The magnetic susceptibility is studied by the methods of series analysis for the one-dimensional border model (a special case of the continuous-spin Ising model). The structure of this model is analyzed and two conjugate pairs of singularities are found near the real (physical) temperature axis. All the numerical results are consistent with the previously known rigorous results, but do not add to the knowledge of the critical properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01112756
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  • 4
    Electronic Resource
    Electronic Resource
    Ising-Model, Block-Spin Distributions by the Markov Property Method (1998)
    Springer
    Journal of statistical physics 93 (1998), S. 573-582 
    Details
    ISSN: 1572-9613
    Keywords: Scaling ; Ising model ; Markov property ; critical phenomena ; parallel computational procedures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The idea that near the critical point each block of spins behaves just like a single big spin is investigated. The case where a diamond-shaped block of spins is embedded in a (small) sea of spins is studied. Use is made of the Markov property method to make exact computations of the various spin moments needed to test this hypothesis. The residual fluctuation about the mean value of the block spin is seen to tend to a finite fraction of the length of the mean block-spin. This result is in line with previous studies which used different types of boundary conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/B:JOSS.0000033242.95755.4e
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  • 5
    Electronic Resource
    Electronic Resource
    The Markov property method applied to Ising model calculations (1994)
    Springer
    Journal of statistical physics 77 (1994), S. 955-976 
    Details
    ISSN: 1572-9613
    Keywords: Markov property ; Ising model ; critical phenomena ; parallel computational procdures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An efficient method of computation for models possessing the Markov property is set out. We apply this method to the two-dimensional ising model and report exact computations for up to 10 by 10 models with periodic boundary conditions. We find that critical-point, finite-size rounding is quite large in the renormalized coupling constant, which is not divergent at the critical point, in contrast to the energy, which is also not divergent and has no rounding there. The difference is traced to the continuity of the energy and the discontinuity of the renormalized coupling constant at the critical point.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02183146
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