Multicriticality of the (2+1) -dimensional gonihedric model: A realization of the (d,m) = (3,2) Lifshitz point

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Abstract

Multicriticality of the gonihedric model in 2+1 dimensions is investigated numerically. The gonihedric model is a fully frustrated Ising magnet with finely tuned plaquette-type (four-body and plaquette-diagonal) interactions, which cancel out the domain-wall surface tension. Because the quantum-mechanical fluctuation along the imaginary-time direction is simply ferromagnetic, the criticality of the (2+1) -dimensional gonihedric model should be an anisotropic one; that is, the respective critical indices of real-space (⊥) and imaginary-time (||) sectors do not coincide. Extending the parameter space to control the domain-wall surface tension, we analyze the criticality in terms of the crossover (multicritical) scaling theory. By means of the numerical diagonalization for the clusters with N≤28 spins, we obtained the correlation-length critical indices (ν ⊥, ν ||) = [0.45 (10), 1.04 (27)], and the crossover exponent =0.7 (2). Our results are comparable to (ν ⊥, ν ||) = (0.482,1.230), and =0.688 obtained by Diehl and Shpot for the (d,m) = (3,2) Lifshitz point with the -expansion method up to O (2).

Original languageEnglish
Article number051116
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume75
Issue number5
DOIs
Publication statusPublished - May 22 2007

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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