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Nature of the glassy transition in simulations of the ferromagnetic plaquette Ising model.

  • Davatolhagh, S
  • Dariush, D
  • Separdar, L
Published Article
Physical Review E
American Physical Society
Publication Date
Mar 01, 2010
3 Pt 1
PMID: 20365734


The homogeneous plaquette Ising model in two and three dimensions is investigated by means of Monte Carlo simulations. By introducing a suitable order parameter for the two-dimensional lattice, and the finite-size scaling of the corresponding fourth-order cumulant, it is found that, consistent with the previous theoretical indications, the model in two dimensions is disordered at finite temperature and exhibits a zero-temperature phase transition characteristic of the one-dimensional Ising model with an essential (exponential) singularity of the order-parameter susceptibility as opposed to a Curie-law (power-law) divergence. In three dimensions, however, the model is believed to have a first-order phase transition at Tc approximately 3.6 screened by strong metastability leading to a so-called "glassy transition" at T approximately 3.4 when subjected to slow cooling. By computing the configurational entropy Sc identical withS(liquid)-S(crystal) in the supercooled temperature range via thermodynamic integration of the internal energy results, the Kauzmann temperature defined as that temperature where the extrapolated configurational entropy Sc(T) vanishes, is estimated to be TK approximately 3.18 . By finding ways to estimate the equilibration time of the supercooled liquid and the nucleation time of the stable crystal droplets, it is shown that T approximately 3.4 is indeed the limit of stability or the effective spinodal temperature Tsp, at which the two time-scales associated with the quasiequilibration of the supercooled liquid, taueq, and the nucleation of the stable crystal droplets, taunuc, cross one another, with the former rising above the latter such that the supercooled liquid state becomes physically irrelevant below Tsp approximately 3.4 and the impending entropy crisis at TK approximately 3.18 (<Tsp) is thus avoided. Hence, what is sometimes called "glassy temperature," is really a kinetic spinodal temperature that may be regarded as the remnant of the mean-field spinodal.

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