First and Continuous Order Phase Transition in the XY-Model in Two Orthogonal Fields

Oluwaseyi Oshin, Kunle Adegoke, Adenike Olatinwo +1 more

Tian Wang, T. L. Chen

A generalized XY model with interaction is studied by Monte Carlo renormalization group method on two-dimensional random triangle lattice. For , a line of fixed points has been found. It characterizes that there is a Kosterlitz-Thouless phase transition. For , a first order phase transition has been found. Both of them show the relationship between the nature of phase transition and the class of interactions.

Jae-Kwon Kim

Kun Hu, Xintian Wu

The wetting transition in the transverse-field spin-$\frac{1}{2}$ XY model with opposite boundary fields ${h}_{L}^{x}{h}_{R}^{x}<0$ is studied analytically and numerically. We find that the phase diagram is complex and that the wetting transition is of three types: first, second, and fourth order. The energy gap is obtained analytically, and the magnetization profile, correlation functions, and wetting layer thickness are obtained numerically. For $|{h}_{L}^{x}|,|{h}_{R}^{x}|<{h}_{w}$, a first-order phase transition occurs at ${h}_{L}^{x}=\ensuremath{-}{h}_{R}^{x}$, where ${h}_{w}$ is the continuous wetting transition point. For $|{h}_{R}^{x}|$ larger than ${h}_{w}$, the continuous wetting transition occurs at ${h}_{L}^{x}={h}_{w}$, and vice versa. For $g\ensuremath{\ne}1\ensuremath{-}{\ensuremath{\gamma}}^{2}$, the wetting transition is second order, and commensurate and incommensurate phases occur for $g<1\ensuremath{-}{\ensuremath{\gamma}}^{2}$ and $g>1\ensuremath{-}{\ensuremath{\gamma}}^{2}$, respectively. For $g=1\ensuremath{-}{\ensuremath{\gamma}}^{2}$, the wetting transition is fourth order. For this fourth-order phase transition, the third derivative of the surface magnetization oscillates and diverges near the transition point. The correlation length exponent is $\ensuremath{\nu}=2$, and the dynamic exponent is $z=2$. Thus, this fourth-order transition belongs to a new universality class. The wetting behavior is induced by asymmetric boundary fields ${h}_{L}^{x}=\ensuremath{-}{h}_{R}^{x}$ and its finite-size scaling is discussed.

Jooyoung Lee, Enzo Granato, J. Michael Kosterlitz

We study, by a Migdal-Kadanoff approximation and Monte Carlo simulations, the phase diagram of a two-dimensional coupled XY-Ising model. This model can describe phase transitions in different systems with underlying continuous and ${\mathit{Z}}_{2}$ symmetries. Depending on the parameters, we find separate XY, Ising and first-order transitions. Also, a line of continuous transitions is found with simultaneous loss of XY and Ising order and varying critical exponents. The fully frustrated XY and Josephson-junction systems can be considered to lie along different paths in the model which can result in nonuniversal behavior if the transition is a single one.

Snehadri Bihari Ota, Smita Ota