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The influence of external boundary conditions on the spherical model of a ferromagnet. I. Magnetization profiles

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Abstract

The spherical model of a ferromagnet is investigated for various (external) boundary conditions. It is shown that, besides the well-known critical point, a second one can be produced by the boundary conditions. Although the main asymptotic of the free energy is analytic at the new critical point, theO(N1−2/d) asymptotic possesses a singularity here. A natural order parameter of the model has singularities at both critical points. The magnetization profile is studied for the whole range of the model's parameters and at different scales. It is shown that (in an appropriate regime) below the second critical temperature the magnetization profile freezes, that is, becomes temperature independent. Distributions of the single spin variables and some macroscopic observables (including normalized total spin) are studied for the whole temperature range including the critical points.

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Patrick, A.E. The influence of external boundary conditions on the spherical model of a ferromagnet. I. Magnetization profiles. J Stat Phys 75, 253–295 (1994). https://doi.org/10.1007/BF02186289

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Key Words

  • Spherical model
  • magnetization profile
  • Gibbs states
  • phase transitions