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Physics Letters A

Numerical evidence for Kosterlitz-Thouless transition in the 2D XY Villain model

Wolfhard Janke E, Klaus Nather

Published Jul 1, 1991• 41 citations
Publisher
DOI
10.1016/0375-9601(91)90401-s

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Monte Carlo study of the Villain version of the fully frustrated XY model

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The fully frustrated XY model with Villain interaction on a square lattice is studied by means of Monte Carlo simulations. On the basis of the universal jump condition it is argued that there are two distinct transitions in the model, corresponding to the loss of XY order and ${\mathrm{Z}}_{2}$ order, respectively. The Kosterlitz-Thouless (KT) transition is analyzed by finite-size scaling of the helicity modulus at lattices of size L=32 through 128, giving ${\mathrm{T}}_{\mathrm{KT}}$\ensuremath{\approx}0.8108(1). The vorticity-vorticity correlation function is used to determine two different characteristic lengths, the ${\mathrm{Z}}_{2}$ correlation length \ensuremath{\xi}, and the screening length \ensuremath{\lambda}, associated with the KT transition and free vortices. The temperature dependence of \ensuremath{\xi} is examined in order to determine ${\mathrm{T}}_{\mathrm{c}}$ and the correlation length exponent, \ensuremath{\nu}. The exponent is found to be consistent with the two-dimensional (2D) Ising value, \ensuremath{\nu}=1, and the obtained critical temperature is ${\mathrm{T}}_{\mathrm{c}}$=0.8225(5). The determinations of both \ensuremath{\xi} and \ensuremath{\nu} are done carefully, first applying the techniques to the 2D Ising model, which serves as a convenient testing ground.

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Critical properties of XY model on two-layer Villain–ferromagnetic lattice

Wang Yi, R. Quartu, Xiaoyan Liu +2 more

We investigate phase transitions of the XY model on a two-layer square lattice which consists of a Villain plane ( J ) and a ferromagnetic plane ( I ), using Monte Carlo simulations and a histogram method. Depending on the values of interaction parameters ( I , J ), the system presents three phases: namely, a Kosterlitz–Thouless (KT) phase in which the two planes are critical for I predominant over J , a chiral phase in which the two planes have a chiral order for J predominant over I and a new phase in which only the Villain plane has a chiral order and the ferromagnetic plane is paramagnetic with a small value of chirality. We clarify the nature of phase transitions by using a finite size scaling method. We find three different kinds of transitions according to the values of ( I , J ): the KT transition, the Ising transition and an XY -Ising transition with ν = 0.849(3). It turns out that the Ising or XY -Ising transition is associated with the disappearance of the chiral order in the Villain plane.

Chinese Physics•Feb 1, 2004•1 citation
The fully frustrated XY model with Villain interaction on a square lattice is studied by means of Monte Carlo simulations. On the basis of the universal jump condition it is argued that there are two distinct transitions in the model, corresponding to the loss of XY order and Z2{\mathrm{Z}}_{2}Z2​ order, respectively. The Kosterlitz-Thouless (KT) transition is analyzed by finite-size scaling of the helicity modulus at lattices of size L=32 through 128, giving TKT{\mathrm{T}}_{\mathrm{KT}}TKT​\ensuremath{\approx}0.8108(1). The vorticity-vorticity correlation function is used to determine two different characteristic lengths, the Z2{\mathrm{Z}}_{2}Z2​ correlation length \ensuremath{\xi}, and the screening length \ensuremath{\lambda}, associated with the KT transition and free vortices. The temperature dependence of \ensuremath{\xi} is examined in order to determine Tc{\mathrm{T}}_{\mathrm{c}}Tc​ and the correlation length exponent, \ensuremath{\nu}. The exponent is found to be consistent with the two-dimensional (2D) Ising value, \ensuremath{\nu}=1, and the obtained critical temperature is Tc{\mathrm{T}}_{\mathrm{c}}Tc​=0.8225(5). The determinations of both \ensuremath{\xi} and \ensuremath{\nu} are done carefully, first applying the techniques to the 2D Ising model, which serves as a convenient testing ground.
We investigate phase transitions of the XY model on a two-layer square lattice which consists of a Villain plane ( J ) and a ferromagnetic plane ( I ), using Monte Carlo simulations and a histogram method. Depending on the values of interaction parameters ( I , J ), the system presents three phases: namely, a Kosterlitz–Thouless (KT) phase in which the two planes are critical for I predominant over J , a chiral phase in which the two planes have a chiral order for J predominant over I and a new phase in which only the Villain plane has a chiral order and the ferromagnetic plane is paramagnetic with a small value of chirality. We clarify the nature of phase transitions by using a finite size scaling method. We find three different kinds of transitions according to the values of ( I , J ): the KT transition, the Ising transition and an XY -Ising transition with ν = 0.849(3). It turns out that the Ising or XY -Ising transition is associated with the disappearance of the chiral order in the Villain plane.