Ghulghazaryan R G, Ananikian N S, Sloot P M A
Department of Theoretical Physics, Yerevan Physics Institute, Alikhanian Brothers 2, 375036 Yerevan, Armenia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Oct;66(4 Pt 2):046110. doi: 10.1103/PhysRevE.66.046110. Epub 2002 Oct 14.
The Yang-Lee zeros of the Q-state Potts model on recursive lattices are studied for noninteger values of Q. Considering one-dimensional (1D) lattice as a Bethe lattice with coordination number equal to 2, the location of Yang-Lee zeros of 1D ferromagnetic and antiferromagnetic Potts models is completely analyzed in terms of neutral periodical points. Three different regimes for Yang-Lee zeros are found for Q>1 and 0<Q<1. An exact analytical formula for the equation of phase transition points is derived for the 1D case. It is shown that Yang-Lee zeros of the Q-state Potts model on a Bethe lattice are located on arcs of circles with the radius depending on Q and temperature for Q>1. Complex magnetic field metastability regions are studied for the Q>1 and 0<Q<1 cases. The Yang-Lee edge singularity exponents are calculated for both 1D and Bethe lattice Potts models. The dynamics of metastability regions for different values of Q is studied numerically.
针对Q的非整数值，研究了递归晶格上Q态Potts模型的杨 - 李零点。将一维（1D）晶格视为配位数等于2的贝塞耳晶格，从中性周期点的角度全面分析了1D铁磁和反铁磁Potts模型的杨 - 李零点位置。对于Q>1和0<Q<1，发现了杨 - 李零点的三种不同情况。推导了1D情况下相变点方程的精确解析公式。结果表明，对于Q>1，贝塞耳晶格上Q态Potts模型的杨 - 李零点位于半径取决于Q和温度的圆弧上。研究了Q>1和0<Q<1情况下的复磁场亚稳区。计算了1D和贝塞耳晶格Potts模型的杨 - 李边缘奇点指数。数值研究了不同Q值下亚稳区的动力学。
