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  • Articles  (5)
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  • Ising model  (5)
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  • Springer  (5)
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  • Physics  (5)
  • Natural Sciences in General
  • 1
    Electronic Resource
    Electronic Resource
    Field theory of the two-dimensional Ising model: Equivalence to the free particle one-dimensional Dirac equation (1973)
    Springer
    Journal of statistical physics 8 (1973), S. 265-278 
    Details
    ISSN: 1572-9613
    Keywords: Field theory ; Ising model ; Dirac equation ; continuum limit ; logarithmic specific heat ; critical behavior ; phase transition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The Schultz-Mattis-Lieb fermion formulation of the two-dimensional Ising model is simplified by means of long-wavelength approximations which become exact in the critical region. The resulting continuum theory has a Hamiltonian density which is shown to be identical, to within a perfect derivative, to that of free, spinless particles satisfying the one-dimensional Dirac equation. Filling the negative-energy single-particle states of momentumq and massκ gives an integral over the single-particle energies -(θ 2+k2)1/2. Becauseκ varies linearly with the temperature, differentiating twice gives Onsager's logarithmic singularity in the specific heat.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01012571
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  • 2
    Electronic Resource
    Electronic Resource
    Two-component ising chain with nearest-neighbor interaction (1973)
    Springer
    Journal of statistical physics 8 (1973), S. 309-333 
    Details
    ISSN: 1572-9613
    Keywords: Ising model ; disordered system ; one-dimensional chain
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The one-dimensional, two-component linear Ising chain with nearest-neighbor interaction is formulated by using the transfer matrix method, with emphasis placed on the case in which the two components are randomly distributed along the chain. Certain recurrence formulas appear such that themth-order partition function of one of the components is dependent on the lower-order ones. The algorithm provides a working basis for discussing the thermodynamic and magnetic functions with various concentrations of one of the components. An exact expression for the partition function is derived for a linear chain which is composed of a periodic distribution of the two components. The construction of a periodic sequence which would approximate a random distribution of the two components is briefly discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01020270
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  • 3
    Electronic Resource
    Electronic Resource
    Nonclassical behavior of the van der Waals gas (1973)
    Springer
    Journal of statistical physics 7 (1973), S. 213-224 
    Details
    ISSN: 1572-9613
    Keywords: Critical behavior ; van der Waals gas ; droplet model of condensation ; Ising model ; functional integration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The partition function of the van der Waals gas is represented by a functional integral which is evaluated by summing the value of the integrand over its absolute and all of its secondary maxima. This leads to a one-to-one correspondence with the Ising model with nearest-neighbor interactions only. Whereas the classical behavior of the van der Waals gas is due to the absolute maximum in function space, the nonclassical behavior is shown to derive from the combined contribution of all the secondary maxima. The relation of this work to inverse range expansions and to the droplet model of condensation is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01030304
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  • 4
    Electronic Resource
    Electronic Resource
    Generating functionals and the Ising model (1973)
    Springer
    Journal of statistical physics 7 (1973), S. 197-212 
    Details
    ISSN: 1572-9613
    Keywords: Correlation functions ; functional formalism ; Ising model ; integral solutions ; saddle point approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The Ising model is studied by the generating functional approach in order to provide a better understanding of that method. It is shown how to derive a general solution of a functional equation in terms of infinite-dimensional integrals. This solution is not unique; the different possibilities are characterized by different paths of integration. Further, the saddle point approximation is used for the integrals in order to obtain second-order correlation functions. It is shown that besides the “normal” solution, one obtains several anomalous ones, which correspond directly to the nonphysical solutions of the transfer matrix method for treating the partition function. It is also shown that only the correct solution can give a realistic behavior of the correlation function at large distances. The relevance of the saddle point methods for describing phase transitions is also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01030303
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  • 5
    Electronic Resource
    Electronic Resource
    Exactly soluble magnetoelastic lattice with a magnetic phase transition (1973)
    Springer
    Journal of statistical physics 7 (1973), S. 337-360 
    Details
    ISSN: 1572-9613
    Keywords: Magnetoelastic system ; phase transition ; renormalization of critical exponents ; Ising model ; statistical mechanics ; soluble models ; thermodynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We examine the soluble magnetoelastic Ising model developed by Baker and Essam and give a detailed discussion of its thermodynamic properties. Particular attention is devoted to the properties of the magnetic phase transition at zero field, which is found to be either first order or second order, depending on whether the experiment is performed at negative or positive pressure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01014909
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