Physical review. B, Condensed matter

Monte Carlo study of the surface special transition in theXYmodel in three dimensions

Pawel Peczak, David Paul Landau

Published Jan 1, 1991• 23 citations

Abstract

Using extensive Monte Carlo simulations we studied the behavior of L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}D films containing classical spins interacting via nearest-neighbor XY interaction. Applying finite-size-scaling analysis and the cumulant method to determine the position of the surface transition boundary, we locate the multicritical point and extract appropriate critical exponents. We present evidence that the surface transition is of the Kosterlitz-Thouless type.

DOI: 10.1103/physrevb.43.1048

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Physical review. B, Condensed matter

Monte Carlo study of the surface special transition in theXYmodel in three dimensions

Pawel Peczak, David Paul Landau

Published Jan 1, 1991• 23 citations

Publisher

Abstract

DOI: 10.1103/physrevb.43.1048

Related papers

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We study the special point in the phase diagram of a semi-infinite system where the bulk transition is in the three-dimensional Ising universality class. To this end we performed a finite-size-scaling study of the improved Blume-Capel model on the simple cubic lattice with two different types of surface interaction. In order to check for the effect of leading bulk corrections we also simulated the spin-1/2 Ising model on the simple cubic lattice. We accurately estimated the surface enhancement coupling at the special point of these models. We find ${y}_{{t}_{1}}=0.718(2)$ and ${y}_{{h}_{1}}=1.6465(6)$ for the surface renormalization group exponents of the special transition. These results are compared with previous ones obtained by using field-theoretic methods and Monte Carlo simulations of the spin-1/2 Ising model. Furthermore, we study the behavior of the surface transition near the special point, and finally we discuss films with special boundary conditions at one surface and fixed ones at the other.We study the special point in the phase diagram of a semi-infinite system where the bulk transition is in the three-dimensional Ising universality class. To this end we performed a finite-size-scaling study of the improved Blume-Capel model on the simple cubic lattice with two different types of surface interaction. In order to check for the effect of leading bulk corrections we also simulated the spin-1/2 Ising model on the simple cubic lattice. We accurately estimated the surface enhancement coupling at the special point of these models. We find ${y}_{{t}_{1}}=0.718(2)$ and ${y}_{{h}_{1}}=1.6465(6)$ for the surface renormalization group exponents of the special transition. These results are compared with previous ones obtained by using field-theoretic methods and Monte Carlo simulations of the spin-1/2 Ising model. Furthermore, we study the behavior of the surface transition near the special point, and finally we discuss films with special boundary conditions at one surface and fixed ones at the other.

arXiv:1108.2425Physical Review BOct 7, 201131 citations

\mathrm{XY}

coupling. The coupling constant

{J}_{S}

for spins in the surface layer is fixed at

0.5J

. Finite-size scaling is used to analyze data for

D=59

and to extract estimates for the surface critical exponents. We find that ${\ensuremath{\beta}}_{1}$ is in good agreement with theoretical predictions.

We report Monte Carlo simulations of Villain's periodic Gaussian XY model on

{\mathit{L}}^{2}

\ifmmode\times\else\texttimes\fi{}N lattices of film geometry (L\ensuremath{\gg}N) with up to N=16 layers, employing the single-cluster update algorithm combined with improved estimators for measurements. The boundary conditions are periodic within each layer and free at the bottom and top layer. Based on data for the specific heat, the spin-spin correlation function, and the susceptibility in the high-temperature phase we study the crossover from three- to two-dimensional behavior as criticality is approached. For the transition temperatures, determined from Kosterlitz-Thouless fits to the correlation length and susceptibility, we observe a pronounced scaling behavior with N. The associated critical exponent, however, deviates from theoretical expectations. More qualitatively, we further discuss the distribution and shapes of vortex loops in the crossover region.

{\mathit{J}}_{\mathit{s}}

. The surface-bulk multicritical point is located with improved precision,

{\mathit{J}}_{\mathit{s}}

/J=1.52\ifmmode\pm\else\textpm\fi{}0.02, and crossover behavior is studied. New estimates for critical exponents are extracted, ${\ensuremath{\gamma}}_{1}$=0.78\ifmmode\pm\else\textpm\fi{}0.06, ${\ensuremath{\gamma}}_{1}^{\mathit{m}}$=1.41\ifmmode\pm\else\textpm\fi{}0.14, ${\ensuremath{\gamma}}_{11}^{\mathit{m}}$=0.96\ifmmode\pm\else\textpm\fi{}0.09, and along with critical amplitude ratios these are compared with theoretically predicted values.

{y}_{{t}_{1}}=0.718(2)

and

{y}_{{h}_{1}}=1.6465(6)

for the surface renormalization group exponents of the special transition. These results are compared with previous ones obtained by using field-theoretic methods and Monte Carlo simulations of the spin-1/2 Ising model. Furthermore, we study the behavior of the surface transition near the special point, and finally we discuss films with special boundary conditions at one surface and fixed ones at the other.