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Random-bond Ising chain in a transverse magnetic field: A finite-size scaling analysis

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We investigate the zero-temperature quantum phase transition of the randombond Ising chain in a transverse magnetic field. Its critical properties are identical to those of the McCoy-Wu model, which is a classical Ising model in two dimensions with layered disorder. The latter is studied via Monte Carlo simulations and transfer matrix calculations and the critical exponents are determined with a finite-size scaling analysis. The magnetization and susceptibility obey conventional rather than activated scaling. We observe that the order parameter and correlation function probability distribution show a nontrivial scaling near the critical point, which implies a hierarchy of critical exponents associated with the critical behavior of the generalized correlation lengths.

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Crisanti, A., Rieger, H. Random-bond Ising chain in a transverse magnetic field: A finite-size scaling analysis. J Stat Phys 77, 1087–1098 (1994). https://doi.org/10.1007/BF02183154

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Key Words

  • Disordered systems
  • quantum spins
  • McCoy-Wu model
  • finite-size scaling
  • anisotropic correlations
  • Monte Carlo simulations
  • products of random matrices