中国物理B ›› 2004, Vol. 13 ›› Issue (2): 251-257.doi: 10.1088/1009-1963/13/2/022

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

R. Quartu1, 堀口刚1, 刘晓彦2, 韩汝琦2, 王漪3   

  1. (1)Department of Computer and Mathematical Sciences, GSIS, Tohoku University 04, Sendai 980-8579, Japan; (2)Institute of Microelectronics, Peking University, Beijing 100871, China; (3)Institute of Microelectronics, Peking University, Beijing 100871, China; Department of Computer and Mathematical Sciences, GSIS, Tohoku University 04, Sendai 980-8579, Japan
  • 收稿日期:2003-05-16 修回日期:2003-07-14 出版日期:2004-02-06 发布日期:2005-07-06
  • 基金资助:
    Project supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, and the National Natural Science Foundation of China (Grant No 10234010).

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

Wang Yi (王漪)ab, R. Quartub, Liu Xiao-Yan (刘晓彦)a, Han Ru-Qi (韩汝琦)a, Horiguchi Tsuyoshi (堀口刚)b    

  1. a Institute of Microelectronics, Peking University, Beijing 100871, China; b Department of Computer and Mathematical Sciences, GSIS, Tohoku University 04, Sendai 980-8579, Japan
  • Received:2003-05-16 Revised:2003-07-14 Online:2004-02-06 Published:2005-07-06
  • Supported by:
    Project supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, and the National Natural Science Foundation of China (Grant No 10234010).

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摘要： 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.

关键词: XY model, chirality, KT transition, two-layer Villain lattice

Abstract: 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 $\nu=0.849(3)$. It turns out that the Ising or XY-Ising transition is associated with the disappearance of the chiral order in the Villain plane.

Key words: XY model, chirality, KT transition, two-layer Villain lattice

中图分类号:  (Classical spin models)

  • 75.10.Hk
75.40.Cx (Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.)) 05.70.Fh (Phase transitions: general studies) 05.50.+q (Lattice theory and statistics) 75.30.Kz (Magnetic phase boundaries (including classical and quantum magnetic transitions, metamagnetism, etc.))