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  • 1
    Electronic Resource
    Electronic Resource
    Partition function zeros in two-dimensional lattice models of the polymer +θ-point (1986)
    s.l. : American Chemical Society
    Macromolecules 19 (1986), S. 2377-2379 
    Details
    ISSN: 1520-5835
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ma00163a007
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The Yang-Lee edge singularity in spherical models (1978)
    Springer
    Journal of statistical physics 19 (1978), S. 205-218 
    Details
    ISSN: 1572-9613
    Keywords: Yang-Lee zeros ; spherical models ; complex magnetic field ; ferromagnets ; critical point singularities ; critical exponents
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The density of Yang-Lee zeros in the thermodynamic limit is discussed for ferromagnetic spherical models of general dimensionalities and arbitrary range of interaction. In all cases the zeros lie on the imaginary axis in the complex magnetic field planeH=H′+iH″ with a densityℊ (H″) that exhibits a square root singularityℊ(H″) ∼(H″-H 0)σ, withσ=1/2, as the edge of the gap atH″=H 0(T) is approached forT〉T c. WhenT→T c one hasH 0(T)∼(T∼T c )Δ with critical exponentΔ=β+γ.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01011723
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    The Yang-Lee edge singularity in one-dimensional Ising andN-vector models (1983)
    Springer
    Journal of statistical physics 30 (1983), S. 15-35 
    Details
    ISSN: 1572-9613
    Keywords: Yang-Lee zeros ; complex magnetic field ; one-dimensional models ; transfer operators
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The distribution of zeros of the partition function in the complex magnetic field plane is studied for linear chains ofn-vector spins and finite-width strips of Ising spins with nearest-neighbor interactions. By means of transfer matrix/operator techniques, the exponent σ characterizing the behavior of the density of zeros near the Yang-Lee edge is shown to have the exact valuea =−1/2 (i) analytically forn-vector chains in the high-temperature limit and for Ising strips in the low-temperature limit, and (ii) numerically for intermediate temperatures. The crossover of σ from itsn-vector value to its spherical model value, σ = 1/2, asn → ∞, as well as fromd = 1 tod = 2 Ising as the width of the strips increases, seems to proceed by an accumulation of branch points in the spectrum of the transfer operator; for then-vector models the position of the gap edge and the free energy at the edge approach their spherical model values with corrections of order l/n ζ with ζ ≅ 3/4.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01010866
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Failures of local approximation in finite-element methods (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1483-1494 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is shown that standard finite-element discretizations of second-order differential equations (i.e. Galerkin and subdomain methods) using conforming linear elements may fail to approximate the original equation locally if the finite-element grid is irregular or if subdomains are chosen improperly. This failure of local approximation can lead to spurious computational results when subdomain methods are used, but these difficulties can be averted by a judicious choice of subdomains. The conditions which the subdomains must satisfy in order for local approximation to hold are derived and used to construct an algorithm for choosing them properly. The relation of these local results to the global convergence properties of the Galerkin method is discussed.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230806
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