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Application of a constrained-transfer-matrix method to metastability in the d = 2 Ising ferromagnet

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  • Günther, C.C.A.
  • Rikvold, P.A.
  • Novotny, M.A.

Abstract

Applying a numerical transfer-matrix formalism, we obtained complex-valued constrained free energies for the two-dimensional square-lattice nearest-neighbor Ising ferromagnet below its critical temperature and in an external magnetic field. In particular, we study the imaginary part of the constrained free-energy branch that corresponds to the metastable phase. Although droplets are not introduced explicitly, the metastable free energy is obtained in excellent agreement with field-theoretical droplet-model predictions. The finite-size scaling properties are different in the weak-field and intermediate-field regimes, and we identify the corresponding different critical-droplet shapes. For intermediate fields, we show that the surface free energy of the critical droplet is given by a Wuff construction with the equilibrium surface tension. We also find a prefactor exponent in complete agreement with the field-theoretical droplet model. Our results extend the region of validity for known results of this field-theoretical droplet model, and they indicate that this transfer-matrix approach provides a nonperturbative numerical continuation of the equilibrium free energy into the metastable phase.

Suggested Citation

  • Günther, C.C.A. & Rikvold, P.A. & Novotny, M.A., 1994. "Application of a constrained-transfer-matrix method to metastability in the d = 2 Ising ferromagnet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 212(1), pages 194-229.
    • Handle: RePEc:eee:phsmap:v:212:y:1994:i:1:p:194-229
    DOI: 10.1016/0378-4371(94)90147-3
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