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Ground-state structure of diluted antiferromagnets and random field systems

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  • Hartmann, Alexander K.

Abstract

A method is presented for the calculation of all exact ground states of diluted Ising antiferromagnets and random field Ising systems in an arbitrary range of magnetic fields Bϵ [Bstart, Bend] resp. Δϵ [Δstart, Δend]. It works by calculating all jump-fields B, Δ where the system changes its ground state. For each field value, all degenerated ground states are represented by a set of (anti-) ferromagnetic clusters and a relation between the clusters. So a complete description of the ground-state structure of these systems is possible. Systems are investigated up to size 483 on the whole field-range and up to 1603 for some particular fields. The behavior of order parameters is investigated, the number of jumps is analyzed and the degree of degeneracy as functions of size and fields is calculated.

Suggested Citation

  • Hartmann, Alexander K., 1998. "Ground-state structure of diluted antiferromagnets and random field systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 248(1), pages 1-20.
    • Handle: RePEc:eee:phsmap:v:248:y:1998:i:1:p:1-20
    DOI: 10.1016/S0378-4371(97)00443-3
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    References listed on IDEAS

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    1. Aharony, Joseph, 1979. "Time Effects in Empirical Stock Valuation Models," The Review of Economics and Statistics, MIT Press, vol. 61(3), pages 460-466, August.
    2. Jost, M. & Usadel, K.D., 1997. "Domain wall roughening in three dimensional magnets at the depinning transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 239(4), pages 486-492.
    3. Maurice Queyranne, 1980. "Theoretical Efficiency of the Algorithm “Capacity” for the Maximum Flow Problem," Mathematics of Operations Research, INFORMS, vol. 5(2), pages 258-266, May.
    4. Hartmann, A.K. & Usadel, K.D., 1995. "Exact determination of all ground states of random field systems in polynomial time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 214(2), pages 141-152.
    5. Nowak, U & Usadel, K.D, 1992. "Correlations and fractality in random Ising magnets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 203-207.
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